Cho A=1/2+1/3+1/4+…+1/63+1/64.chứng tỏ rằng A>3

Đáp án:

Giải thích các bước giải:

`A=1/2+1/3+1/4+…+1/63+1/64`

`= 1 + 1 /2 + ( 1 /3 + 1 /4 ) +  ⋅ ⋅ ⋅ + ( 1/ 33 + 1/ 34 + ⋅ ⋅ ⋅ + 1 /64 )>1 + 1 /2 + ( 1 /4 + 1/ 4 ) + ⋅ ⋅ ⋅ + ( 1/ 64 + ⋅ ⋅ ⋅ + 1/ 64 )= 1 + 1 /2 + 2 ⋅ 1 /4 + 4 ⋅ 1 /8 + 8 ⋅ 1 /16 + 16 ⋅ 1/ 32 + 32 ⋅ 1 /64= 1 + 1/ 2 + 1/ 2 + 1/ 2 + 1 /2 + 1 2/ + 1/ 2 = 4`

Do `A>4` mà `4>3`

`=>A>3`