Question

Chứng minh rằng : 1/26+1/27+1/28+.......+1/50=1-1/2+1/3-1/4+.....+1/49-

1/50

Answer 1

Ta có :1/26 + 1/27 + ... + 1/50 - (1-1/2+1/3-1/4+...+1/49-1/50) 
=1/26+1/27+...+1/50 + (1/26-1/27+....-1/49+1/50) + (-1/13+1/14-....+1/24-1/25)+(-1/7+1/8-..... + 1/12) + (1/6-1/5+1/4)+(1/2-1) 
=1/13+1/14+...+1/25+ (-1/13+1/14-....+1/24-1/25)+(-1/7+1/8-..... + 1/12) + (1/6-1/5+1/4)+(1/2-1) 
=1/7+1/8+...+1/12 + (-1/7+1/8-...-1/11 + 1/12) + (1/6-1/5+1/4)+(1/2-1) 
=1/4+1/5+1/6 +(1/6-1/5+1/4)+(1/2-1) 
=1/2+1/2-1 
=0 
Vậy 1/26 + 1/27 + 1/28 +.....+ 1/49 +1/50 = 1- 1/2 +1/3 - 1/4 +....+ 1/49 - 1/50