Question

[Nguyệt Mạc]

CMR: 1/26 + 1/27 + 1/28 + ... + 1/50 = 1 - 1/2 + 1/3 - 1/4 + ... + 1/49 - 1/50 

gấpp ạaaa

Answer 1

[Akai Haruma]

Lời giải:
Ta có:
$1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{49}-\frac{1}{50}$

$=(1+\frac{1}{3}+\frac{1}{5}+....+\frac{1}{49})-(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50})$

$=(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+....+\frac{1}{49}+\frac{1}{50})-2(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50})$

$=(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+....+\frac{1}{49}+\frac{1}{50})-(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{25})$

$=\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}$