Tính Nhanh

A= 5/2.4+5/4.6+5/6.8+...+5/98.100

So sánh

C=3/2+3/6+3/12+...+3/600 và3

`A = 5/(2 . 4) + 5/(4 . 6) + 5/(6 . 8) + ... + 5/(98 . 100)`

`A = 5/2 . ( 2/(2 . 4) + 2/(4 . 6) + 2/(6 . 8) + ... + 2/(98 . 100) )`

`A = 5/2 . ( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/98 - 1/100 )`

`A = 5/2 . ( 1/2 - 1/100 )`

`A = 5/2 . 49/100`

`A = 49/40`

$\\$

Ta có: `C = 3/2 + 3/6 + 3/12 + ... + 3/600`

`C = 3/(1 . 2) + 3/(2 . 3) + 3/(3 . 4) + ... + 3/(24 . 25)`

`C = 3 . ( 3/(1 . 2) + 3/(2 . 3) + 3/(3 . 4) + ... + 3/(24 . 25) )`

`C = 3 . ( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/24 - 1/25 )`

`C = 3 . ( 1 - 1/25 )`

`C = 3 . 24/25`

`C = 72/25 = 2,88`

Vì `2,88 < 3`

nên `C < 3`