The Answer to the Question
is below this banner.
Here's the Solution to this Question
For any natural number n, prove the validity of given series by mathematical induction:
Let be the proposition that for the first positive integers
BASIS STEP: is true, because
INDUCTIVE STEP: For the inductive hypothesis we 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
We have that
We show 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 any natural number