2n+1 > (n + 2) · sin(n)
Let be the proposition
Basis Step. is true, because
Inductive Step.
Assume that holds for an arbitrary positive integer That is, we assume that
Under this assumption, it must be shown that is true, namely, that
This shows that is true under the assumption that is true. This completes the inductive step.
We have completed the basis step and the inductive step, so by mathematical induction we know that is true for all positive integers That is, we have proven that for all positive integers
Then for all positive integers
We have proven that for all positive integers
Therefore we have proven that
for all positive integers
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