Question

A=2/1x3+2/3x5+2/5x7+....+2/99x101

Tính bằng cách thuận tiện.

Answer 1

\(A=\frac{3-1}{1.3}+\frac{5-3}{3.5}+...+\frac{101-99}{99.101}\)

\(A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}=\frac{100}{101}\)