How to prove the following inequality: $$\forall n\geqslant 4:\dfrac {3^{n}+4^{n}+\cdots +\left( n+2\right) ^{n}} {\left( n+3\right) ^{n}} < 1$$
inequality with sum of powers
3
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algebra-precalculus
inequality
discrete-mathematics
induction
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0It looks like the last term in the numerator should be $(n+2)^n$ and the denominator should be $(n+3)^n$. This is what Sasha answered. – 2012-07-18