Đáp án+Giải thích các bước giải:
a) A= $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + ... + $\frac{1}{99.100}$
= $\frac{1}{1}$ - $\frac{1}{2}$ + $\frac{1}{2}$ - $\frac{1}{3}$ + ... + $\frac{1}{99}$ - $\frac{1}{100}$
= 1 - $\frac{1}{100}$
= $\frac{99}{100}$
Vậy A = $\frac{99}{100}$
b) B = $\frac{1}{1.3}$ + $\frac{1}{3.5}$ + ... + $\frac{1}{99.101}$
=>2B = $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + ... + $\frac{2}{99.101}$
= $\frac{1}{1}$ - $\frac{1}{3}$ + $\frac{1}{3}$ - $\frac{1}{5}$ + ... + $\frac{1}{99}$ - $\frac{1}{101}$
= 1 - $\frac{1}{101}$
= $\frac{100}{101}$
=> B = $\frac{50}{101}$
Vậy B = $\frac{50}{101}$
Xin ctlhn
