Đáp án:
1/2^2 + 1/4^2 + 1/6^2 +...+1/100^2>1/2(đpcm)`
Giải thích các bước giải:
`A = 1/2^2 + 1/4^2 + 1/6^2 +...+1/100^2 > 1/2 `
Ta có :
`1/2 < 1/1.2 `
` 1/4< 1/2.4 `
`1/6 < 1/4.6 `
`....`
`1/100^2 < 1/99.100`
`=> 1/2^2 + 1/4^2 + 1/6^2 +...+1/100^2 > 1/1.2 + 1/2.4 + 1/4.6 +... + 1/98.100`
`=>1/2^2 + 1/4^2 + 1/6^2 +...+1/100^2> 1/1 - 1/2+1/2 - 1/4 + 1/4 - 1/6 +...+ 1/98 - 1/100`
`=>1/2^2 + 1/4^2 + 1/6^2 +...+1/100^2> 1/1 - 1/100`
`=>1/2^2 + 1/4^2 + 1/6^2 +...+1/100^2>99/100>1/2`
Do ` 1/2 = 50/100`
Mà ` 99/100 > 50/100`
Vậy`1/2^2 + 1/4^2 + 1/6^2 +...+1/100^2>1/2(đpcm)`
