Question

\(\frac{9}{10}\) +       \(\frac{39}{40}\) +            \(\frac{87}{88}\) +   ...       +             \(\frac{1119}{1120}\)

Ai nhanh và đúng nhất mk sẽ tick cho!

Answer 1

Ta có : 

\(\frac{9}{10}+\frac{39}{40}+\frac{87}{88}+...+\frac{1119}{1120}\)

\(=\)\(\left(1-\frac{1}{10}\right)+\left(1-\frac{1}{40}\right)+\left(1-\frac{1}{88}\right)+...+\left(1-\frac{1}{1120}\right)\)

\(=\)\(\left(1+1+1+...+1\right)-\left(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+...+\frac{1}{1120}\right)\)

\(=\)\(\left(1+1+1+...+1\right)-\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{32.35}\right)\)

\(=\)\(11-\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{32}-\frac{1}{35}\right)\)

\(=\)\(11-\left(\frac{1}{2}-\frac{1}{35}\right)\)

\(=\)\(11-\frac{33}{70}\)

\(=\)\(\frac{737}{70}\)

Chúc bạn học tốt ~