So sánh:
a) \(\frac{-3}{1.3}+\frac{-3}{3.5}+...+\frac{-3}{97.99}\)và \(\frac{49}{-20}\)
b)\(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}và\frac{99}{202}\)
c)\(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}và\frac{99}{100}\)
Những câu hỏi liên quan
Tìm x, biết:
a. \(\left(\frac{2}{1.3}+\frac{2}{3.5}+....+\frac{2}{97.99}\right)-x=\frac{-100}{99}\)
b. \(2+\frac{2}{3}+\frac{2}{6}+\frac{2}{7}+.......+\frac{2}{x.\left(x+1\right)}=1\frac{1989}{1991}\)
1/TÍNH NHANHa/ frac{left(2^3.5.7right).left(5^2.7^3right)}{left(2.5.7^2right)^2}2/so sánha/frac{2009}{2010}vafrac{2010}{2011} b/frac{1}{3^{400}}vafrac{1}{4^{300}} c/frac{200}{201}+frac{201}{202}vafrac{200+201}{201+202} d/frac{2008}{2008+2009}vafrac{2009}{2009+2010}3/TÌM X BIẾTleft(frac{2}{1.3}+frac{2}{3.5}+frac{2}{5.7}+....+frac{2}{97.99}right)-xfrac{-100}{99}GIÚP MÌNH NHA MAI MÌNH NỘP RÙI
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1/TÍNH NHANH
a/ \(\frac{\left(2^3.5.7\right).\left(5^2.7^3\right)}{\left(2.5.7^2\right)^2}\)
2/so sánh
a/\(\frac{2009}{2010}va\frac{2010}{2011}\) b/\(\frac{1}{3^{400}}va\frac{1}{4^{300}}\) c/\(\frac{200}{201}+\frac{201}{202}va\frac{200+201}{201+202}\) d/\(\frac{2008}{2008+2009}va\frac{2009}{2009+2010}\)
3/TÌM X BIẾT
\(\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{97.99}\right)-x=\frac{-100}{99}\)
GIÚP MÌNH NHA MAI MÌNH NỘP RÙI
a/\(\frac{\left(2^3.5.7\right).\left(5^2.7^3\right)}{\left(2.5.7^2\right)^2}\)
=\(\frac{2^3.5^3.7^4}{2^2.5^2.7^4}\)
=2.5
=10
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Bài 1: Tính hợp lí (nếu có thể) Bài 2:Tìm x biết
a, left(4frac{2}{3}-1frac{1}{6}right):left(1,75+1frac{1}{2}right) a, frac{4}{9}+xfrac{-5}{3}
b, frac{11}{53}+left(frac{32}{47}+frac{-10}{53}right)+frac{-64}{94}+frac{1}{-53}+frac{1}{3} b, 2,4:left(frac{1}{2}.x-frac{3}{4}right)frac{3}{10}
c, 125% -7frac{1}{2}+0,5:frac{4}{3} c, frac{x+1}{-8}frac{-2}{x+1}...
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Bài 1: Tính hợp lí (nếu có thể) Bài 2:Tìm x biết
a, \(\left(4\frac{2}{3}-1\frac{1}{6}\right):\left(1,75+1\frac{1}{2}\right)\) a, \(\frac{4}{9}+x=\frac{-5}{3}\)
b, \(\frac{11}{53}+\left(\frac{32}{47}+\frac{-10}{53}\right)+\frac{-64}{94}+\frac{1}{-53}+\frac{1}{3}\) b, 2,4:\(\left(\frac{1}{2}.x-\frac{3}{4}\right)=\frac{3}{10}\)
c, 125% -7\(\frac{1}{2}+0,5:\frac{4}{3}\) c, \(\frac{x+1}{-8}=\frac{-2}{x+1}\)
d, 1\(\frac{1}{20}.\left(\frac{-2}{3}\right)^2+\left(0,8-\frac{8}{15}\right):\frac{-4}{17}\) d, \(\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)-x=\frac{-100}{99}\)
Bài 2:
a) \(\frac{4}{9}+x=\frac{-5}{3}\)
\(\Leftrightarrow x=\frac{-5}{3}-\frac{4}{9}\)
\(\Leftrightarrow x=\frac{-15}{9}-\frac{4}{9}\)\(=\frac{-19}{9}\)
Vậy: \(x=\frac{-19}{9}\)
b) \(2,4:\left(\frac{1}{2}.x-\frac{3}{4}\right)=\frac{3}{10}\)
\(\Leftrightarrow\frac{24}{10}:\left(\frac{1}{2}x-\frac{3}{4}\right)=\frac{3}{10}\)
\(\Leftrightarrow\frac{1}{2}x-\frac{3}{4}=\frac{24}{10}:\frac{3}{10}=\frac{24}{10}.\frac{10}{3}\)\(=8\)
\(\Leftrightarrow\frac{1}{2}x=8+\frac{3}{4}=\frac{35}{4}\)
\(\Leftrightarrow x=\frac{35}{4}:\frac{1}{2}=\frac{35}{4}.2=\frac{35}{2}\)
c) \(\frac{x+1}{-8}=\frac{-2}{x+1}\)
\(\Rightarrow\left(x+1\right).\left(x+1\right)=\left(-2\right).\left(-8\right)\)
\(\Leftrightarrow\left(x+1\right)^2=16=4^2=\left(-4\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x+1=4\\x+1=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)
Vậy: \(x\in\left\{3;-5\right\}\)
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Tính nhanh
1,
A = \(\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+..........+\frac{1}{97.99}-\frac{1}{98.100}\)
2,
B=
\(1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+.........+\frac{1}{20}.\left(1+2+3+.........+20\right)\)
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
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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
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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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)
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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 =\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{99}\right)\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{100-99}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}=\frac{99}{100}\)
\(B=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)
\(B=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{101-99}{99.101}\)
\(B=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(B=1-\frac{1}{101}=\frac{100}{101}\)
\(C=\frac{3^2}{10}+\frac{3^2}{40}+\frac{3^2}{88}+...+\frac{3^2}{340}\)
\(C=3\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\right)\)
\(C=3\left(\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+...+\frac{20-17}{17.20}\right)\)
\(C=3\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right)\)
\(C=3\left(\frac{1}{2}-\frac{1}{20}\right)=\frac{27}{20}\)
\(D=\frac{7}{1.3}+\frac{7}{3.5}+\frac{7}{5.7}+...+\frac{7}{99.101}\)
\(D=\frac{7}{2}B=\frac{7}{2}.\frac{100}{101}=\frac{350}{101}\)
\(E=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
\(3E=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)
\(3E-E=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)
\(2E=1-\frac{1}{3^8}\)
\(E=\frac{3^8-1}{2.3^8}\)
\(G=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{99}\right)\)
\(G=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{98}{99}=\frac{1}{99}\)
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Tính:
a) \(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}...\frac{99^2}{99.100}.\frac{100^2}{100.101}\)
b)\(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{59^2}{58.60}\)
a,1^2/1.2 . 2^2/2.3 . 3^2/3.4 ... 99^2/99.100 . 100^2/100.101
= 1/2 . 2/3 . 3/4 ... 99/100 . 100/101
=( 2.3.4....100/2.3.4...100) . 1/101
= 1 . 1/101
=1/101
ý b tương tự nhé !
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Bạn kia đéo biết thì thôi xen vào làm gì?
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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
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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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