### Home > PC > Chapter 8 > Lesson 8.2.6 > Problem 8-152

8-152.

Copy the steps below and fill in the blanks to prove that * *for

*. Note that we do not start with*

*. Verify that the statement is false for*

*.*

Verify the statement is true for

.whereas . Assume the statement is true for

.Assume that

for.Prove the statement is true for

.Recall that:

We assumed that

, therefore. Because

,and hence ____.

Following the steps from above, we have shown that ________. Prove the statement is true for

.Recall that:

We assumed that

, therefore. Because

,and hence. Following the steps from above, we have shown that

.

Write a conclusion for your proof by induction.

Hence, by mathematical induction we have proven that

for.