A =1/2 mũ 2 + 1/4 mũ 2 + 1/6 mũ 2 + ……..+ 1/100 mũ 2. CMR a<1/2 13/08/2021 Bởi Elliana A =1/2 mũ 2 + 1/4 mũ 2 + 1/6 mũ 2 + ……..+ 1/100 mũ 2. CMR a<1/2
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)` Bình luận
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)`