Prove-that-ln-n-1-lt-1-1-2-1-1-2-2-2-1-n-2-n-n-N-

Tinku Tara June 4, 2023 None 0 Comments

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Question Number 189394 by TUN last updated on 15/Mar/23

Prove that: ln(n+1)<(1/( (√(1^2 +1))))+(1/( (√(2^2 +2))))+...+(1/( (√(n^2 +n))))(∀n∈N^∗ )

P r o v e t h a t :

l n (n + 1) < \frac{1}{\sqrt{1^{2} + 1}} + \frac{1}{\sqrt{2^{2} + 2}} + \dots + \frac{1}{\sqrt{n^{2} + n}} (\forall n \in N^{*})

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