tính
\(\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+...+\frac{127}{128}-6\)
Những câu hỏi liên quan
\(\frac{\frac{1}{4}+\frac{1}{24}+\frac{1}{124}}{\frac{3}{4}+\frac{3}{24}+\frac{3}{124}}+\frac{\frac{2}{7}+\frac{2}{17}+\frac{2}{127}}{\frac{3}{7}+\frac{3}{17}+\frac{3}{127}}\)
\(\frac{\frac{1}{4}+\frac{1}{24}+\frac{1}{124}}{\frac{3}{4}+\frac{3}{24}+\frac{3}{124}}+\frac{\frac{2}{7}+\frac{2}{17}+\frac{2}{127}}{\frac{3}{7}+\frac{3}{17}+\frac{3}{127}}=\frac{\frac{1}{4}+\frac{1}{24}+\frac{1}{124}}{3\left(\frac{1}{4}+\frac{1}{24}+\frac{1}{124}\right)}+\frac{2\left(\frac{1}{7}+\frac{1}{17}+\frac{1}{127}\right)}{3\left(\frac{1}{7}+\frac{1}{17}+127\right)}=\frac{1}{3}+\frac{2}{3}=\) \(1\)
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Tính : a) \(\frac{1}{9}\div\frac{8}{27}\times-3\div\frac{81}{128}\)
b) \(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right)\times230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{7}+\frac{10}{3}\right)\div\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
Tính nhanh :
\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}\)
\(D=\frac{1}{2}+\frac{-1}{5}+\frac{-5}{7}+\frac{1}{6}+\frac{-3}{35}+\frac{1}{3}+\frac{1}{41}\)
\(E=\frac{-1}{2}+\frac{3}{5}+\frac{-1}{9}+\frac{1}{127}+\frac{-7}{18}+\frac{4}{35}+\frac{2}{7}\)
C = 1/3 + -3/4 + 3/5 + 1/57 + -1/36 + 1/15 + -2/9
C = ( 1/3 + 1/57 ) + ( -3/4 + -1/36 ) + ( 3/5 + 1/15 ) + -2/9
C = ( 19/57 + 1/57 ) + ( -27/36 + -1/36 ) + ( 9/15 + 1/15 ) + -2/9
C = 20/57 + -28/36 + 10/15 + -2/9
C = 20/57 + -7/9 + 2/3 + -2/9
C = ( 20/57 + 2/3 ) + ( -7/9 + -2/9 )
C = 58/57 + -1
C = 1/57
D = 1/2 + -1/5 + -5/7 + 1/6 + -3/35 + 1/3 + 1/41
D = ( 1/2 + 1/3 + 1/6 ) + ( -1/5 + -5/7 +-3/35 ) + 1/41
D = ( 3/6 + 2/6 + 1/6 ) + ( -7/35 + -25/35 + -3/35 ) + 1/41
D = 1 + -1 + 1/41
D = 1/41
E = -1/2 + 3/5 + -1/9 + 1/127 + -7/18 + 4/35 + 2/7
E = ( -1/2 + -1/9 + -7/18 ) + ( 3/5 + 4/35 ) + 1/127 + 2/7
E = ( -9/18 + -2/18 + -7/18 ) + ( 21/35 + 4/35 ) + 1/127 + 2/7
E = -1 + 5/7 + 1/257 + 2/7
E = -1 + ( 5/7 + 2/7 ) + 1/127
E = -1 + 1 + 1/127
E = 1/127
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\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}.\)
\(C=\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)-\left(\frac{3}{4}+\frac{1}{36}+\frac{2}{9}\right)+\frac{1}{57}\)
\(C=1-1+\frac{1}{57}\)
\(C=\frac{1}{57}\)
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D=1/2+-1/5+-5/7+1/6+-3/35+1/3+1/41
D=(1/2+1/6+1/3)-(1/5+3/35+5/7)+1/41
D=1-1+1/41
D=1/41
E=-1/2+3/5+-1/9+1/127+-7/18+4/35+2/7
E=(3/5+4/35+2/7)-(1/2+1/9+7/18)+1/127
E=1-1+1/127
E=1/127
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Tính hợp lý
\(\frac{\frac{5}{3}+\frac{5}{8}-\frac{5}{7}}{\frac{-4}{3}-\frac{-4}{8}+\frac{4}{7}}:\frac{\frac{2}{3}-\frac{1}{6}+\frac{6}{7}}{\frac{-1}{3}+\frac{1}{6}-\frac{1}{7}}\)
\(=\frac{5\left(\frac{1}{3}+\frac{1}{8}-\frac{1}{7}\right)}{-4\left(\frac{1}{3}+\frac{1}{8}-\frac{1}{7}\right)}:\frac{2\left(\frac{1}{3}-\frac{1}{12}+\frac{3}{7}\right)}{ }\)
MÃu thứ hai sao ý
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Tính nhanh: \(\frac{3}{1!+2!+3!}+\frac{4}{2!+3!+4!}+\frac{5}{3!+4!+5!}+\frac{6}{4!+5!+6!}+\frac{7}{5!+6!+7!}+\frac{8}{6!+7!+8!}\)
Đặt P = ... ( biểu thức đề bài )
Nhận xét: Với \(k\inℕ^∗\) ta có:
\(\frac{k+2}{k!+\left(k+1\right)!+\left(k+2\right)!}=\frac{k+2}{k!+\left(k+1\right).k!+\left(k+2\right).k!}=\frac{k+2}{2.k!\left(k+2\right)}=\frac{1}{2.k!}\)
\(\Rightarrow\)\(P=\frac{1}{2.1!}+\frac{1}{2.2!}+...+\frac{1}{2.6!}=\frac{1}{2}\left(1+\frac{1}{2}+...+\frac{1}{720}\right)=...\)
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So sánh:frac{frac{frac{1}{2}}{frac{3}{4}}}{frac{frac{5}{6}}{frac{7}{8}}}+frac{frac{frac{8}{7}}{frac{6}{5}}}{frac{frac{4}{3}}{frac{2}{1}}} vàfrac{frac{frac{1}{2}}{frac{3}{4}}+frac{frac{8}{7}}{frac{6}{5}}}{frac{frac{5}{6}}{frac{7}{8}}+frac{frac{4}{3}}{frac{2}{1}}}và frac{frac{frac{1}{2}+frac{8}{7}}{frac{3}{4}+frac{6}{5}}}{frac{frac{5}{6}+frac{4}{3}}{frac{7}{8}+frac{2}{1}}}vàfrac{frac{frac{1+8}{2+7}}{frac{3+6}{4+5}}}{frac{5+4}{frac{6+3}{2+1}}}
Đọc tiếp
So sánh:\(\frac{\frac{\frac{1}{2}}{\frac{3}{4}}}{\frac{\frac{5}{6}}{\frac{7}{8}}}+\frac{\frac{\frac{8}{7}}{\frac{6}{5}}}{\frac{\frac{4}{3}}{\frac{2}{1}}}\) và\(\frac{\frac{\frac{1}{2}}{\frac{3}{4}}+\frac{\frac{8}{7}}{\frac{6}{5}}}{\frac{\frac{5}{6}}{\frac{7}{8}}+\frac{\frac{4}{3}}{\frac{2}{1}}}\)và \(\frac{\frac{\frac{1}{2}+\frac{8}{7}}{\frac{3}{4}+\frac{6}{5}}}{\frac{\frac{5}{6}+\frac{4}{3}}{\frac{7}{8}+\frac{2}{1}}}\)và\(\frac{\frac{\frac{1+8}{2+7}}{\frac{3+6}{4+5}}}{\frac{5+4}{\frac{6+3}{2+1}}}\)
1. Tính:
\(S=\frac{1+2^2+2^3+...+2^{2008}}{1-2^{2009}}\); \(P=\frac{1+4+7+11+...+127}{\frac{2}{4}.\frac{6}{9}.\frac{12}{16}...\frac{420}{400}}\)
Cho A = 1 + 2 + 22 + 23 + ... + 22008
-> 2A = 2 + 22 + 23 + 24 +...+ 22009
-> 2A - A = ( 2 + 22 + 23 + 24 +...+ 22009 ) - ( 1 + 2 + 22 + 23 + ... + 22008 )
-> A = \(2^{2009}-1=-\left(1-2^{2009}\right)\)
S = \(\frac{-\left(1-2^{2009}\right)}{1-2^{2009}}\)=-1
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Tính nhanh :
\(-\frac{1}{2}-\left(-\frac{3}{5}\right)+\left(-\frac{1}{9}\right)+\frac{1}{127}-\frac{7}{18}+\frac{4}{35}-\left(-\frac{2}{7}\right)\)
\(-\frac{1}{2}-\left(-\frac{3}{5}\right)+\left(-\frac{1}{9}\right)+\frac{1}{127}-\frac{7}{18}+\frac{4}{35}-\left(-\frac{2}{7}\right)\)
\(=-\frac{1}{2}+\frac{3}{5}-\frac{1}{9}+\frac{1}{127}-\frac{7}{18}+\frac{4}{35}+\frac{2}{7}\)
\(=\left(-\frac{1}{2}-\frac{1}{9}-\frac{7}{18}\right)+\left(\frac{3}{5}+\frac{4}{35}+\frac{2}{7}\right)+\frac{1}{127}\)
\(=\left(-\frac{9}{18}-\frac{2}{18}-\frac{7}{18}\right)+\left(\frac{21}{35}+\frac{4}{35}+\frac{10}{35}\right)+\frac{1}{127}\)
\(=\frac{-18}{18}+\frac{35}{35}+\frac{1}{127}=-1+1+\frac{1}{127}=\frac{1}{127}\)
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Tính
a) \(\frac{1}{5}+\frac{-1}{6}+\frac{1}{7}+\frac{1}{-8}+\frac{1}{9}+\frac{1}{8}+\frac{1}{-7}+\frac{-1}{6}+\frac{-1}{5}\)
b) (-11).36-64.11
c) \(\frac{\frac{1}{3}+\frac{1}{7}+\frac{1}{13}}{\frac{2}{3}+\frac{2}{7}+\frac{2}{13}}.\frac{\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\frac{3}{256}}{1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}}+\frac{3}{8}\)
