chứng minh: 1/4+1/16+1/36+…+1/10000<1/2 05/08/2021 Bởi Adalyn chứng minh: 1/4+1/16+1/36+…+1/10000<1/2
Đáp án: tham khảo ạ≈ω Giải thích các bước giải: `1/4+1/16+1/36+…+1/10000<1/2` `A= 1/4. ( 1/1 + 1/4 + 1/9 + …+ 1/2500)` `A<1/4.(1/1 + 1/2.2 + 1/3.3+…+1/50.50)` `A<1/4.(1/1 + 1/1 – 1/2 +1/2 – 1/3+….+1/49 – 1/50)` `A<1/4.(1/1+1/1 – 1/50)` `A<1/(4).(99)/(50)` `A<99/200` Mà ` 1/2=100/200` Do `A=99<100` `=> A=99/200<100/200` `=>A=1/4+1/16+1/36+…+1/10000<1/2(đpcm)` Bình luận
Đáp án:
tham khảo ạ≈ω
Giải thích các bước giải:
`1/4+1/16+1/36+…+1/10000<1/2`
`A= 1/4. ( 1/1 + 1/4 + 1/9 + …+ 1/2500)`
`A<1/4.(1/1 + 1/2.2 + 1/3.3+…+1/50.50)`
`A<1/4.(1/1 + 1/1 – 1/2 +1/2 – 1/3+….+1/49 – 1/50)`
`A<1/4.(1/1+1/1 – 1/50)`
`A<1/(4).(99)/(50)`
`A<99/200`
Mà ` 1/2=100/200`
Do `A=99<100`
`=> A=99/200<100/200`
`=>A=1/4+1/16+1/36+…+1/10000<1/2(đpcm)`