TÍNH:[/:phần]
a)1/2 - 1/3 + 1/4 -1/5 + 1/6 - 1/7 +1/5 - 1/4 + 1/3 - 1/2
b)1/2 + 1/6 + 1/12 +1/20+ 1/30
c)\(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+\(\frac{2}{5.7}\)+...+\(\frac{2}{47.49}\)
d)\(\frac{4}{1.5}\)+\(\frac{4}{5.9}\)+...+\(\frac{4}{41.45}\)
Những câu hỏi liên quan
1) Thực hiện phép tínha)frac{2}{1.4}+frac{2}{4.7}+frac{2}{7.10}+...+frac{2}{91.94}+frac{2}{94.97}b)left(13frac{1}{4}-2frac{5}{27}-10frac{5}{6}right).230frac{1}{25}+46frac{3}{4}PHẦNleft(1frac{3}{7}+frac{10}{3}right):left(12frac{1}{3}-14frac{2}{7}right) 2)Tìm x:a)frac{1}{1.3}+frac{1}{3.5}+frac{1}{5.7}+...+frac{1}{x.left(x+2right)}frac{1005}{2011}
Đọc tiếp
1) Thực hiện phép tính
a)\(\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{91.94}+\frac{2}{94.97}\)
b)\(\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}\)PHẦN
\(\left(1\frac{3}{7}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)\)
2)Tìm x:
a)\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x.\left(x+2\right)}=\frac{1005}{2011}\)
Bài nhìn vô muốn xỉu rồi ='((
1. a) \(\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{91.94}+\frac{2}{94.97}\)
\(=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{91.94}+\frac{3}{94.97}\right)\)
\(=\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{94}-\frac{1}{97}\right)\)
\(=\frac{2}{3}\left(1-\frac{1}{97}\right)=\frac{2}{3}.\frac{96}{97}=\frac{64}{97}\)
b) Bạn tự làm, làm nữa chắc xỉu =((( Khi nào rảnh mình sẽ làm, nếu bạn cần
2 )
a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{1005}{2011}\)
\(\Leftrightarrow\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{1005}{2011}\)
\(\Leftrightarrow\frac{1}{2}\left(1-\frac{1}{x+2}\right)=\frac{1005}{2011}\)
\(\Leftrightarrow1-\frac{1}{x+2}=\frac{1005}{2011}:2=\frac{1005}{4022}\)
\(\Leftrightarrow\frac{1}{x+2}=1-\frac{1005}{4022}=\frac{3017}{4020+2}\)
\(\Rightarrow x=4020\)
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Tìm x biết
a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{47.49}=\frac{24}{x+1}\)
b) \(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{97.101}=\frac{2x+4}{101}\)
c) \(\frac{x-1}{2017}+\frac{x-2}{2016}=\frac{x-3}{2015}+\frac{x-4}{2014}\)
d) \(\frac{x+1}{2017}+\frac{x+2}{2016}=\frac{x+3}{2015}+\frac{x+4}{2014}\)
\(b)\) \(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{97.101}=\frac{2x+4}{101}\)
\(\Leftrightarrow\)\(\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{97}-\frac{1}{101}=\frac{2x+4}{101}\)
\(\Leftrightarrow\)\(1-\frac{1}{101}=\frac{2x+4}{101}\)
\(\Leftrightarrow\)\(\frac{100}{101}=\frac{2x+4}{101}\)
\(\Leftrightarrow\)\(100=2x+4\)
\(\Leftrightarrow\)\(2x=96\)
\(\Leftrightarrow\)\(48\)
Vậy \(x=48\)
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\(a)\) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{47.49}=\frac{24}{x+1}\)
\(\Leftrightarrow\)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{47.49}=\frac{48}{x+1}\)
\(\Leftrightarrow\)\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{47}-\frac{1}{49}=\frac{48}{x+1}\)
\(\Leftrightarrow\)\(1-\frac{1}{49}=\frac{48}{x+1}\)
\(\Leftrightarrow\)\(\frac{48}{49}=\frac{48}{x+1}\)
\(\Leftrightarrow\)\(49=x+1\)
\(\Leftrightarrow\)\(x=48\)
Vậy \(x=48\)
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tínhA frac{11}{1.3}+ frac{47}{3.5}+ frac{107}{5.7}+ frac{191}{7.9}+...+ frac{971}{17.19}B frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}- frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3-5^9.7^3.2^3}C 1.3+3.5+5.7+...+ (2n-1)(2n+1)Giúp mình vs nhanh nhanh nha các bạn
Đọc tiếp
tính
A =\(\frac{11}{1.3}\)+ \(\frac{47}{3.5}\)+ \(\frac{107}{5.7}\)+ \(\frac{191}{7.9}\)+...+ \(\frac{971}{17.19}\)
B = \(\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}\)- \(\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3-5^9.7^3.2^3}\)
C = 1.3+3.5+5.7+...+ (2n-1)(2n+1)
Giúp mình vs nhanh nhanh nha các bạn
bài 1 thực hiện phép tính, tính nhanh nếu có thểa, frac{-11}{23}.frac{6}{7}+frac{8}{7}.frac{-11}{23}-frac{1}{23}b,0,75.1frac{7}{9}-1frac{2}{5}:frac{-21}{20}c,2.frac{3}{7}+left(frac{2}{9}-1frac{3}{7}right)-frac{5}{3}:frac{1}{9}d,11frac{1}{4}-left(2frac{5}{7}+5frac{1}{4}right)e,left(6-2frac{4}{5}right).3frac{1}{8}-1frac{3}{5}:25%g,0,2.frac{15}{36}-left(frac{2}{5}+frac{2}{3}right):1frac{1}{5}h,2frac{1}{3}-frac{1}{3}.left(frac{-3}{2}+left(frac{2}{3}+0,4.5right)right)i,frac{1}{3}.frac{5}{7}-frac{7}{2...
Đọc tiếp
bài 1 thực hiện phép tính, tính nhanh nếu có thể
a, \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}\)
b,\(0,75.1\frac{7}{9}-1\frac{2}{5}:\frac{-21}{20}\)
c,\(2.\frac{3}{7}+\left(\frac{2}{9}-1\frac{3}{7}\right)-\frac{5}{3}:\frac{1}{9}\)
d,\(11\frac{1}{4}-\left(2\frac{5}{7}+5\frac{1}{4}\right)\)
e,\(\left(6-2\frac{4}{5}\right).3\frac{1}{8}-1\frac{3}{5}:25\%\)
g,\(0,2.\frac{15}{36}-\left(\frac{2}{5}+\frac{2}{3}\right):1\frac{1}{5}\)
h,\(2\frac{1}{3}-\frac{1}{3}.\left(\frac{-3}{2}+\left(\frac{2}{3}+0,4.5\right)\right)\)
i,\(\frac{1}{3}.\frac{5}{7}-\frac{7}{27}.\frac{36}{14}\)
k,\(\left(\frac{-5}{28}+1,75+\frac{8}{35}\right):\left(-3\frac{9}{20}\right)\)
l,\(\left(20+9\frac{1}{4}\right):2\frac{1}{4}\)
m,\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{12.13}\)
n,\(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{99.101}\)
1/TINH
\(\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}\)
\(\frac{2^3}{1.3}.\frac{3^2}{2.4}.\frac{4^2^{^{^{ }}}}{3.5}......\frac{99^2}{98.100}\)
2/CMR
\(\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+\frac{1}{64}+\frac{1}{100}+\frac{1}{144}+\frac{1}{196}+...+\frac{1}{10000}< \frac{1}{2}\)
1/ Tính:
\(\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}\)
\(=\frac{3}{1.2}-\frac{5}{2.3}+\frac{7}{3.4}-\frac{9}{4.5}+\frac{11}{5.6}-\frac{13}{6.7}+\frac{15}{7.8}-\frac{17}{8.9}+\frac{19}{9.10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(=\frac{9}{10}\)
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a) (frac{1}{2}+frac{1}{6}+frac{1}{12}+frac{1}{20}+...+frac{1}{132}) . x frac{1}{3}
b) (frac{2}{1.3}+frac{2}{3.5}+frac{2}{5.7}+frac{2}{7.9}+frac{2}{9.11}) : x frac{2}{3}
c) (frac{1}{1.3}+frac{1}{3.5}+frac{1}{5.7}+frac{1}{7.9}+frac{1}{9.11}) . x frac{2}{3}
Mik đang cần gấp
Đọc tiếp
a) (\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{132}\)) . x =\(\frac{1}{3}\)
b) (\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)) : x = \(\frac{2}{3}\)
c) (\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)) . x = \(\frac{2}{3}\)
Mik đang cần gấp
a)(\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{11.12}\)). x=\(\frac{1}{3}\)
(1-\(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{11}_{ }+\frac{1}{12}\)).x=\(\frac{1}{3}\)
(1+\(\frac{1}{12}\)).x=\(\frac{1}{3}\)
x=\(\frac{1}{3}:\frac{13}{12}\)
x=\(\frac{4}{13}\)
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b)( \(2-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+...+\frac{2}{9}-\frac{2}{11}_{ }\)):x =\(\frac{2}{3}\)
Giống câu a
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B1 : tínhA 1 + 2 +3 +4+5+...+99+100B frac{1}{2}+ frac{1}{6}+frac{1}{12}+frac{1}{20}+frac{1}{30}+...+frac{1}{9900}B2 : Tính frac{1}{1.3}+frac{1}{3.5}+frac{1}{5.7}+...+frac{1}{2013.2015}B3 :So sánhMfrac{1}{1.2}+frac{1}{2.3}+...+frac{1}{49.50}với 1B4: TínhBfrac{1+2+2^2+2^3+...+2^{2015}}{1-2^{2016}}Mấy bạn làm được bài nào thì chỉ cho mình zới
Đọc tiếp
B1 : tính
A= 1 + 2 +3 +4+5+...+99+100
B =\(\frac{1}{2}\)+ \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{9900}\)
B2 : Tính
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2013.2015}\)
B3 :So sánh
\(M=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)với 1
B4: Tính
\(B=\frac{1+2+2^2+2^3+...+2^{2015}}{1-2^{2016}}\)
Mấy bạn làm được bài nào thì chỉ cho mình zới
Mk giải ko chép lại đề nhá!
Bài 3:
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}\)\(-\frac{1}{50}\)
\(=\frac{1}{1}-\frac{1}{50}\)
\(=\frac{50}{50}-\frac{1}{50}\)
\(=\frac{49}{50}\)
Vậy: M < 1
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Bài 2:
\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2013}-\frac{1}{2015}\)
\(=\frac{1}{1}-\frac{1}{2015}\)
\(=\frac{2015}{2015}-\frac{1}{2015}\)
\(=\frac{2014}{2015}\)
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B1
A co (100-1)+1=100 so hang
A=(100+1).100 :2=5050
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Bài 1: Tính tổng sau :A frac{1}{1.2}+frac{1}{2.3}+frac{1}{3.4}+...+frac{1}{99.100}B frac{2}{1.3}+frac{2}{3.5}+frac{2}{5.7}+...+frac{2}{99.101}C frac{3^2}{10}+frac{3^2}{40}+frac{3^2}{88}+...+frac{3^2}{340}D frac{7}{1.3}+frac{7}{3.5}+frac{7}{5.7}+...+frac{7}{99.101}E frac{1}{3}+frac{1}{3^2}+frac{1}{3^3}+...+frac{1}{3^8}G left(1-frac{1}{2}right).left(1-frac{1}{3}right).left(1-frac{1}{4}right).....left(1-frac{1}{99}right)
Đọc tiếp
Bài 1: Tính tổng sau :
A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
B =\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)
C =\(\frac{3^2}{10}+\frac{3^2}{40}+\frac{3^2}{88}+...+\frac{3^2}{340}\)
D =\(\frac{7}{1.3}+\frac{7}{3.5}+\frac{7}{5.7}+...+\frac{7}{99.101}\)
E =\(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
G =\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{99}\right)\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{100-99}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}=\frac{99}{100}\)
\(B=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)
\(B=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{101-99}{99.101}\)
\(B=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(B=1-\frac{1}{101}=\frac{100}{101}\)
\(C=\frac{3^2}{10}+\frac{3^2}{40}+\frac{3^2}{88}+...+\frac{3^2}{340}\)
\(C=3\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\right)\)
\(C=3\left(\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+...+\frac{20-17}{17.20}\right)\)
\(C=3\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right)\)
\(C=3\left(\frac{1}{2}-\frac{1}{20}\right)=\frac{27}{20}\)
\(D=\frac{7}{1.3}+\frac{7}{3.5}+\frac{7}{5.7}+...+\frac{7}{99.101}\)
\(D=\frac{7}{2}B=\frac{7}{2}.\frac{100}{101}=\frac{350}{101}\)
\(E=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
\(3E=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)
\(3E-E=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)
\(2E=1-\frac{1}{3^8}\)
\(E=\frac{3^8-1}{2.3^8}\)
\(G=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{99}\right)\)
\(G=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{98}{99}=\frac{1}{99}\)
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left(frac{-5}{12}+frac{7}{4}-frac{3}{8}right)-left[4frac{1}{2}-7frac{1}{3}right]-left(frac{1}{4}-frac{5}{2}right)left[2frac{1}{4}-5frac{3}{2}right]-left(frac{3}{10}-1right)-5frac{1}{2}+left(frac{1}{3}-frac{5}{6}right)frac{4}{7}-left(3frac{2}{5}-1frac{1}{2}right)-frac{5}{21}+left[3frac{1}{2}-4frac{2}{3}right]frac{1}{8}-1frac{3}{4}+left(frac{7}{8}-3frac{7}{2}+frac{3}{4}right)-left[frac{7}{4}-frac{5}{8}right]left(frac{3}{5}-2frac{1}{10}+frac{11}{20}right)-left[frac{-3}{4}+1frac{7}{2}right]left[-2fr...
Đọc tiếp
\(\left(\frac{-5}{12}+\frac{7}{4}-\frac{3}{8}\right)-\left[4\frac{1}{2}-7\frac{1}{3}\right]-\left(\frac{1}{4}-\frac{5}{2}\right)\)
\(\left[2\frac{1}{4}-5\frac{3}{2}\right]-\left(\frac{3}{10}-1\right)-5\frac{1}{2}+\left(\frac{1}{3}-\frac{5}{6}\right)\)
\(\frac{4}{7}-\left(3\frac{2}{5}-1\frac{1}{2}\right)-\frac{5}{21}+\left[3\frac{1}{2}-4\frac{2}{3}\right]\)
\(\frac{1}{8}-1\frac{3}{4}+\left(\frac{7}{8}-3\frac{7}{2}+\frac{3}{4}\right)-\left[\frac{7}{4}-\frac{5}{8}\right]\)
\(\left(\frac{3}{5}-2\frac{1}{10}+\frac{11}{20}\right)-\left[\frac{-3}{4}+1\frac{7}{2}\right]\)
\(\left[-2\frac{1}{5}-2\frac{2}{3}\right]-\left(\frac{1}{15}-5\frac{1}{2}\right)+\left[\frac{-1}{6}+\frac{1}{3}\right]\)
\(1\frac{1}{8}-\left(\frac{1}{15}-\frac{1}{2}+\frac{-1}{6}\right)+\left[\frac{5}{4}+\frac{3}{2}\right]\)
\(\frac{5}{6}-\left(1\frac{1}{3}-1\frac{1}{2}\right)+\left[\frac{5}{12}-\frac{3}{4}-\frac{1}{6}\right]\)
\(1\frac{1}{4}-\left(\frac{7}{12}-\frac{2}{3}-1\frac{3}{8}\right)+\left[\frac{5}{24}-2\frac{1}{2}\right]-\frac{1}{6}-\left[\frac{-3}{4}\right]\)
\(-2\frac{1}{5}+2\frac{3}{10}-\left(\frac{6}{20}-\left[\frac{2}{8}-1\frac{1}{2}\right]\right)+\left[\frac{7}{20}-1\frac{1}{4}\right]\)
\(-\left[1\frac{2}{3}-3\frac{1}{2}+\frac{1}{4}\right]+\left(\frac{2}{6}-\frac{5}{12}\right)-\left(\frac{1}{3}-\left[\frac{1}{4}-\frac{1}{3}\right]\right)\)
\(-\frac{4}{5}-\left(1\frac{1}{10}-\frac{7}{10}\right)+\left[\frac{3}{4}-1\frac{1}{5}\right]+1\frac{1}{2}\)
\(\frac{3}{21}-\frac{5}{14}+\left[1\frac{1}{3}-5\frac{1}{2}+\frac{5}{14}\right]-\left(\frac{1}{6}-\frac{3}{7}+\frac{1}{3}\right)\)
\(-1\frac{2}{5}+\left[1\frac{3}{10}-\frac{7}{20}-1\frac{1}{4}\right]-\left(\frac{1}{5}-\left[\frac{3}{4}-1\frac{1}{2}\right]\right)\)
\(2\frac{1}{3}-\left(\frac{1}{2}-2\frac{1}{6}+\frac{3}{4}\right)+\left[\frac{5}{12}-1\frac{1}{3}\right]-\frac{7}{8}+3\frac{1}{2}\)
\(2\frac{1}{4}-1\frac{3}{5}-\left(\frac{9}{20}-\frac{7}{10}\right)+\left[1\frac{3}{5}-2\frac{1}{2}\right]+\frac{3}{4}\)
\(\left[\frac{8}{3}-5\frac{1}{4}+\frac{1}{6}\right]-\frac{7}{4}+\frac{-5}{12}-\left(1-1\frac{1}{2}+\frac{1}{3}\right)\)
\(\left(\frac{1}{4}-\left[1\frac{1}{4}-\frac{7}{10}\right]+\frac{1}{2}\right)-2\frac{1}{5}-1\frac{3}{10}+\left[1-\frac{1}{2}\right]\)
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