Question

A=1/31+1/32+...+1/2048 > 3

Answer 1

A = 1/31 + 1/32 + 1/33 + ... + 1/2048
= (1/31 + 1/32 +...+1/40) + (1/41 + 1/42 +...+1/50) +...+(1/2031 + 1/2032 +..+1/2040)
= 10/40 + 10/50 +...+10/2040
=1/4 + 1/5 +...+1/204
= (1/4 + 1/5 + ... + 1/9) + (1/10 + 1/11 +...+ 1/20) +...+ (1/191 + 1/192 +...+ 1/200)
= (1/4 + 1/5 +...+ 1/9) + 10/20 +...+10/200
= 1/2 + 1/3 + 2(1/4 + 1/5 + .. +1/9) + 1/10 + (1/11 + 1/12+...+ 1/20)
= 5/6 + 2.0,99 + 10/20 > 3
Vậy A > 3 (đpcm)