Question

cmr 1/2+1/2^2+1/3^2+...+1/50^2<1

Answer 1

1/2 + 1/2^2 + 1/3^2 + .....+ 1/50^2 < 1/1 + 1/1.2 + 1/2.3 +...+ 1/49.50

Đặt A = 1/1 + 1/1.2 + 1/2.3 +...+ 1/49.50

A= 1/1 - 1/1 + 1/1 -1/2 + 1/2 -1/3+...+ 1/49-1/50

A= 1/1 - 1/50

A= 49/50

Vì 49/50 < 1 mà 1/2 + 1/2^2 + 1/3^2 + .....+ 1/50^2 < 49/50 nên 1/2 + 1/2^2 + 1/3^2 + .....+ 1/50^2 <1

Vậy....