Proving that: \sum_{n=1}^{99}\frac{\sqrt{n+1}-\sqrt{n}}{2n+1}<\frac{9}{20}

Rome Frazier

Rome Frazier

Answered question

2022-02-25

Proving that:
n=199n+1n2n+1<920

Answer & Explanation

Malaika Ridley

Malaika Ridley

Beginner2022-02-26Added 6 answers

As we known (2n+1)2=4n2+4n+1>4n2+4n=4n(n+1), then
2n+1>2n(n+1), with nN. Hence we have
n=199n+1n2n+1<n=199n+1n2n(n+1)
=12n=1991n1n+1=12(1110)=920

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