Cho A=1+1/2+1/3+1/4.....+1/63. Chứng minh rằng A>3

`A=1+1/2+1/3+1/4+...+1/63`

`A=1+1/2+(1/3+1/4)+(1/5+1/6+1/7+1/8)+...+(1/33+1/34+1/35+...+1/63)`

`A>1+1/2+(1/4+1/4)+(1/8+1/8+1/8+1/8)+...+(1/63+1/63+...+1/63)` ( `31` số hạng `1/63`)

`A>1+1/2+1/2+1/2+...+31/63` ( 5 số hạng`1/2`)

`A>1+1/2 . 5+31/63`

`A>1+2,5+31/63`

`A>3,5+31/63`

 Mà `31/63 >0;3,5>3`

`=>` `A>3`