chứng minh: 1/4+1/16+1/36+…+1/10000<1/2 05/08/2021 Bởi Serenity chứng minh: 1/4+1/16+1/36+…+1/10000<1/2
Đặt `A= 1/4 + 1/16 + 1/36 +…+ 1/10000` `A= 1/4 ( 1 + 1/4 + 1/9 + …+ 1/2500)` `A= 1/4 ( 1 + 1/2.2 + 1/3.3 +…+ 1/50.50)` `A < 1/4 ( 1 + 1/1.2 + 1/2.3 +…+ 1/49.50)` `A< 1/4( 1+ 1/1 – 1/2 + 1/2 -1/3 +… + 1/49 – 1/50)` `A< 1/4 ( 1 + 1 – 1/50)` `A< 1/4 ( 2 – 1/50)` `A< 1/2 – 1/200 < 1/2` Vậy `A< 1/2` Bình luận
đây
Đặt `A= 1/4 + 1/16 + 1/36 +…+ 1/10000`
`A= 1/4 ( 1 + 1/4 + 1/9 + …+ 1/2500)`
`A= 1/4 ( 1 + 1/2.2 + 1/3.3 +…+ 1/50.50)`
`A < 1/4 ( 1 + 1/1.2 + 1/2.3 +…+ 1/49.50)`
`A< 1/4( 1+ 1/1 – 1/2 + 1/2 -1/3 +… + 1/49 – 1/50)`
`A< 1/4 ( 1 + 1 – 1/50)`
`A< 1/4 ( 2 – 1/50)`
`A< 1/2 – 1/200 < 1/2`
Vậy `A< 1/2`