Question

[Sơn Trần]

Giải hộ mìn câu 20 nha

Answer 1

[Akai Haruma]

Câu 20:

\(S=\frac{2}{1.4.7}+\frac{2}{4.7.10}+...+\frac{2}{34.37.40}\)

\(3S=\frac{6}{1.4.7}+\frac{6}{4.7.10}+....+\frac{6}{34.37.40}=\frac{7-1}{1.4.7}+\frac{10-4}{4.7.10}+...+\frac{40-34}{34.37.40}\)

\(=\frac{1}{1.4}-\frac{1}{4.7}+\frac{1}{4.7}-\frac{1}{7.10}+...+\frac{1}{34.37}-\frac{1}{37.40}\)

\(=\frac{1}{1.4}-\frac{1}{37.40}=\frac{369}{1480}\)

$S=\frac{123}{1480}$