Question

[Nguyễn Thế Sơn]

Chứng minh rằng : \(\dfrac{1}{26}+\dfrac{1}{27}+\dfrac{1}{28}+...+\dfrac{1}{50}=1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}+\dfrac{1}{50}\)

Answer 1

[Nguyễn Tuấn Minh]

Ta có :

Vế phải =1 - 1/2 + 1/3 - 1/4 + ... + 1/49 - 1/50

= (1+ 1/3 + 1/5 + ... + 1/49) - (1/2 + 1/4 + ... +1/50)

<=> (1 + 1/2 + 1/3 + 1/4 + ... + 1/49+1/50)- 2(1/2 +1/4 +...+1/50)

=(1+1/2 +1/3 +1/4...+ 1/49+1/50) - (1+1/2 +...+1/25)

=1/26 + 1/27 +1/28 +...+1/50 (đpcm)