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Let be the proposition that for any positive integer
is true, because
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
is also true.
This last equation 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