Đáp án:
`=>A<9/5 ( đpcm)`
Giải thích các bước giải:
Đặt `A=1 + 1/2^2 + 1/3^2 + 1/4^2 +...+1/99^2 + 1/100^2 < 9/5 `
`A =1 + 1/2^2 + 1/3^2 + 1/4^2 +...+1/99^2 + 1/100^2 < 1 + 1/(2.2) + 1/(3.3 ) + 1/(4.4) +....+1/(99.99) + 1/(100.100) < 9/5 `
`A=1 + 1/2^2 + 1/3^2 + 1/4^2 +...+1/99^2 + 1/100^2 < 1+ 1/4 + 1/(2.3) + 1/(3.4) +...+1/(98.99) + 1/(99.100)<9/5`
`A=1 + 1/2^2 + 1/3^2 + 1/4^2 +...+1/99^2 + 1/100^2 < 5/4 + 1/2 - 1/3 - 1/4 +...+ 1/98 + 1/99 + 1/99 - 1/100 <9/5 `
`A=1 + 1/2^2 + 1/3^2 + 1/4^2 +...+1/99^2 + 1/100^2<5/4 + 1/2 - 1/100 < 9/5 `
`A=1 + 1/2^2 + 1/3^2 + 1/4^2 +...+1/99^2 + 1/100^2 <5/4 + 49/100 < 9/5 `
`A=1 + 1/2^2 + 1/3^2 + 1/4^2 +...+1/99^2 + 1/100^2 <87/50 < 9/5 `
DO ` 9/5 = 90/50`
Mà ` 87/50 < 90/50`
`=>A<9/5 ( đpcm)`
