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Homework Statement
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]h2.
Homework Equations
None.
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]h2.
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]h2.