Question

[Thủ Lĩnh Thẻ Bài]

1/50*51+1/51*52+...........+1/99*100

Answer 1

[Đoàn Đức Hà]

\(\frac{1}{50\times51}+\frac{1}{51\times52}+...+\frac{1}{99\times100}\)

\(=\frac{51-50}{50\times51}+\frac{52-51}{51\times52}+...+\frac{100-99}{99\times100}\)

\(=\frac{1}{50}-\frac{1}{51}+\frac{1}{51}-\frac{1}{52}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{50}-\frac{1}{100}=\frac{1}{100}\)