cho A=1/2^2+1/3^2+1/4^2+...+1/9^2 CMR A>2/5

`@` Lời giải:

`A = 1/(2^2) + 1/(3^2) + 1/(4^2) + ... + 1/(9^2)`

Ta có:

`A > 1/(2*3) +1/(3*4) + 1/(4*5) + ... + 1/(9*10)`

Ta có: `1/(2*3) + 1/(3*4) + 1/(4*5) + ... + 1/(9*10)`

`= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10`

`= 1/2 - 1/10`

`= 5/10 - 1/10`

`= 4/10`

`= 2/5`

Mà `A > 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(4*5) + ... + 1/(9*10)`

`=> A > 2/5` (đpcm)