Câu hỏi của Phạm Minh Vũ

Question

1/1×2+1/2×3+1/3×4+...+1/49×50+1/50×51

Đoàn Đức Hà · Accepted Answer

$\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{49\times50}+\frac{1}{50\times51}$

$=\frac{2-1}{1\times2}+\frac{3-2}{2\times3}+\frac{4-3}{3\times4}+...+\frac{50-49}{49\times50}+\frac{51-50}{50\times51}$

$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}+\frac{1}{50}-\frac{1}{51}$

$=1-\frac{1}{51}$

$=\frac{50}{51}$

Câu trả lời:

$\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{49\times50}+\frac{1}{50\times51}$

$=\frac{2-1}{1\times2}+\frac{3-2}{2\times3}+\frac{4-3}{3\times4}+...+\frac{50-49}{49\times50}+\frac{51-50}{50\times51}$

$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}+\frac{1}{50}-\frac{1}{51}$

$=1-\frac{1}{51}$

$=\frac{50}{51}$