The problem is as follows:
Prove that $2 - (2\cdot7) + ((2\cdot7)^2) - ... +(2(-7))^n =
> \frac{(1-(-7)^{(n+1)})}{4}$ whenever $n$ is a non-negative integer.
Our book is asking for a basic inductive proof to show that for any $n$, $n+1$ will also hold.
So far I have the following:
$\frac{1-(-7)^{(n+1)}}{4} + 2(-7)^{(n+1)} =?= \frac{1-(-7)^{(n+2)}}{4}$
I'm a little confused about why these problems are giving me so much trouble. I understand that we will assume (after having proven a base case) that the proof will work for any number k, and in proving this, we will show that any number (k+1) will also hold. Perhaps I'm just setting it up incorrectly or am missing some small algebraic facet.
In any case, if some one can get me going in the right direction, I would really appreciate it.
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