Question

Tính tổng sau:D=9 / 10 - 1 / 90 - 1 / 72 - 1 / 56 - ... -1 / 6 - 1 / 2

Giúp mk nhé!Cảm ơn các bạn nhiều nha!

Answer 1

\(D=\frac{9}{10}-\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-...-\frac{1}{6}-\frac{1}{2}\)

\(=\frac{9}{10}-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)

\(=\frac{9}{10}-\)\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

\(=\frac{9}{10}-\left(1-\frac{1}{10}\right)\)

\(=\frac{9}{10}-1+\frac{1}{10}\)\(=0\)