ta có 1 - 1/3 + 1/3 - 1/5 +1/5 - 1/7 +... +1/n-2 - 1/n=60/61

rút gọn ta còn 1-1/n=60/61

n-1/n=60/61

vậy n= 61

\(A=2-\left(\frac{2^3}{25}+\frac{2^3}{63}+...+\frac{2^3}{255}+\frac{2^3}{323}\right)\)

\(=2-4.\left(\frac{2}{35}+\frac{2}{63}+...+\frac{2}{255}+\frac{2}{323}\right)\)

\(=2-4.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{15.17}+\frac{2}{17.19}\right)\)

\(=2-4.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}\right)\)

\(=2-4.\left(\frac{1}{5}-\frac{1}{19}\right)\)

\(=2-4.\frac{14}{95}=2-\frac{56}{95}=\frac{134}{95}\)

Tính A

\(A=2\frac{2}{35}^3-\frac{2^3}{63}-\frac{2}{99}^3-\frac{2}{143}^3-\frac{2}{195}^3-\frac{2}{255}^3-\frac{2}{323}^3\)

giải cả bài nha

\(A=\frac{2}{35}+\frac{4}{77}+\frac{2}{143}+\frac{4}{221}+\frac{2}{223}+\frac{4}{437}+\frac{2}{575}\)

\(=\frac{2}{5.7}+\frac{2}{7.11}+\frac{2}{11.13}+\frac{4}{13.17}+\frac{2}{17.19}+\frac{4}{19.23}+\frac{2}{23.25}\)

\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}+\frac{1}{23}-\frac{1}{25}\)

\(=\frac{1}{5}-\frac{1}{25}\)

\(=\frac{4}{25}\)

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