Đáp án:
Giải thích các bước giải:
`sqrt{n+1}-sqrt{n}`
`=[(sqrt{n+1}-n)(sqrt{n+1}+sqrt{n})]/(sqrt{n+1}+sqrt{n})`
`=(n+1-n)/(sqrt{n+1}+sqrt{n})`
`=1/(sqrt{n+1}+sqrt{n)`
vì `n<n+1`
`=>sqrt{n}<sqrt{n+1}`
`=>sqrt{n}+sqrt{n+1}<2sqrt{n+1}`
`=>1/(sqrt{n}+sqrt{n+1})>1/(sqrt{n+1})`
hay `sqrt{n+1}-sqrt{n}>1/(sqrt{n+1})(ĐPCM)`