Cho C=1/5+1/13+1/14+1/15+1/61+1/62+1/63 Chứng minh C<1\2 29/10/2021 Bởi Sadie Cho C=1/5+1/13+1/14+1/15+1/61+1/62+1/63 Chứng minh C<1\2
Đáp án: `C<1/2` Giải thích các bước giải: `C=1/5+1/13+1/14+1/15+1/61+1/62+1/63` `=>C=1/5+(1/13+1/14+1/15)+(1/61+1/62+1/63)` Ta thấy `1/12>1/13;1/12>1/14;1/12>1/15` `=>1/13+1/14+1/15<1/12+1/12+1/12` `=>1/13+1/14+1/15<1/4(1)` Ta thấy `1/60>1/61;1/60>1/62;1/60>1/63` `=>1/61+1/62+1/63<1/60+1/60+1/60` `=>1/61+1/62+1/63<1/20(2)` Từ `(1)` và `(2)` ta có: `=>1/13+1/14+1/15+1/61+1/62+1/63<1/4+1/20` `=>1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/5+1/4+1/20` `=>1/5+1/13+1/14+1/15+1/61+1/62+1/63<9/20+1/20` `=>1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/2` Vậy `C<1/2`. Bình luận
Ta có : `1/13 < 1/12` `1/14 < 1/12` `1/15 < 1/12` `1/61 < 1/60 ` `1/62 < 1/60 ` `1/63 < 1/60` ⇒ `1/5+1/13+1/14+1/15+1/61+1/62+1/63 < 1/5 + 1/12 + 1/12 + 1/12 + 1/60 + 1/60 + 1/60` ⇔`C < 1/5 + 3.(1/12) + 3. (1/60)` ⇔`C < 1/5 + 1/4 + 1/20 ` ⇔ `C < 1/2` @Active Activity ##From-IOD## Bình luận
Đáp án:
`C<1/2`
Giải thích các bước giải:
`C=1/5+1/13+1/14+1/15+1/61+1/62+1/63`
`=>C=1/5+(1/13+1/14+1/15)+(1/61+1/62+1/63)`
Ta thấy `1/12>1/13;1/12>1/14;1/12>1/15`
`=>1/13+1/14+1/15<1/12+1/12+1/12`
`=>1/13+1/14+1/15<1/4(1)`
Ta thấy `1/60>1/61;1/60>1/62;1/60>1/63`
`=>1/61+1/62+1/63<1/60+1/60+1/60`
`=>1/61+1/62+1/63<1/20(2)`
Từ `(1)` và `(2)` ta có:
`=>1/13+1/14+1/15+1/61+1/62+1/63<1/4+1/20`
`=>1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/5+1/4+1/20`
`=>1/5+1/13+1/14+1/15+1/61+1/62+1/63<9/20+1/20`
`=>1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/2`
Vậy `C<1/2`.
Ta có :
`1/13 < 1/12`
`1/14 < 1/12`
`1/15 < 1/12`
`1/61 < 1/60 `
`1/62 < 1/60 `
`1/63 < 1/60`
⇒ `1/5+1/13+1/14+1/15+1/61+1/62+1/63 < 1/5 + 1/12 + 1/12 + 1/12 + 1/60 + 1/60 + 1/60`
⇔`C < 1/5 + 3.(1/12) + 3. (1/60)`
⇔`C < 1/5 + 1/4 + 1/20 `
⇔ `C < 1/2`
@Active Activity
##From-IOD##