Câu hỏi của Lê Thu Ngọc

Question

1/1x1/2+1/2x1/3+1/3x1/4+...+1/79x1/80

l҉o҉n҉g҉ d҉z҉ · Accepted Answer

$\frac{1}{1}\cdot\frac{1}{2}+\frac{1}{2}\cdot\frac{1}{3}+\frac{1}{3}\cdot\frac{1}{4}+...+\frac{1}{79}\cdot\frac{1}{80}$

$=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{79\cdot80}$

$=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+...+\frac{1}{79}-\frac{1}{80}$

$=1-\frac{1}{80}$

$=\frac{79}{80}$

Câu trả lời:

$\frac{1}{1}\cdot\frac{1}{2}+\frac{1}{2}\cdot\frac{1}{3}+\frac{1}{3}\cdot\frac{1}{4}+...+\frac{1}{79}\cdot\frac{1}{80}$

$=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{79\cdot80}$

$=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+...+\frac{1}{79}-\frac{1}{80}$

$=1-\frac{1}{80}$

$=\frac{79}{80}$