(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that for any positive h and any integer n[itex]\geq[/itex]0, (1+h)^{n}[itex]\geq[/itex]1+nh+[itex]\frac{n(n+1)}{2}[/itex]h^{2}.

2. Relevant equations

None.

3. The attempt at a solution

I proved that P(0) is true (1[itex]\geq[/itex]1). The rest of the proof goes as follows:

Assume K[itex]\in[/itex]Z(the set of integers) and P(K) is true.

Then (1+h)^{K}[itex]\geq[/itex]1+Kh+[itex]\frac{K(K-1)}{2}[/itex]h^{2}.

Then (1+h)^{(K+1)}= (1+h)^{K}+(1+h)^{1}...

I can't figure out how to relate that part to the final part of P(K+1), which is 1+(K+1)h+[itex]\frac{(K+1)(K+1-1)}{2}[/itex]h^{2}.

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# Proof by Induction

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