Mathematical Induction Problem

[MathInduction]

Here is a problem on mathematical induction, and I just can't solve it. Every single possible solution I tried has come to a dead end because I either
A) can't find another step to do or
B) The logic is warped.
i attached picture as a file because not really sure how else I can type it....

 

[Deleted member 4993]

Here is a problem on mathematical induction, and I just can't solve it. Every single possible solution I tried has come to a dead end because I either
A) can't find another step to do or
B) The logic is warped.
i attached picture as a file because not really sure how else I can type it....

Please share your work (some of your tries) with us - so that we may know where to begin to help you.