Mathematical Induction 1 Prove Statements Using Mathematical Induction

Question

Examlex · Accepted Answer

The Answer is First, we show that the statement is true when n = 1.
For n = 1, we get 1

This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,

is true for some positive integer k.
We need to show that the statement holds for k + 1. That is, we need to show that

So we assume that 1

is true and add the next term,

to both sides of the equation.

Condition II is satisfied. As a result, the statement is true for all natural numbers n.

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