Question

证明:2((根号n+1)-1)

Answer 1

1/√n=2/(√n+√n)＞2/(√n+1+√n)=2(√n+1 -√n)

所以1+1/√2+1/√3+...+1/√n

＞2(√2-1)+2(√3-√2)+2(√4-√3)+...+2(√n+1-√n)

=2(√n+1-1)

右边也一样,1/√n=2/(√n+√n)＜2/(√n-1+√n)=2(√n -√n-1)

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