Câu hỏi của Mạnh Nguyễn

Question

1/1x2 + 1/2x3 + 1/3x4 + ... + 1/99x100 + 1/100x101 = ...

Nguyễn Đăng Nhân · Accepted Answer

$\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{100\cdot101}$

$=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-...+\dfrac{1}{100}-\dfrac{1}{101}$

$=1-\dfrac{1}{101}$

$=\dfrac{100}{101}$Câu trả lời: $\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{100\cdot101}$

$=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-...+\dfrac{1}{100}-\dfrac{1}{101}$

$=1-\dfrac{1}{101}$

$=\dfrac{100}{101}$