Mathematical Induction Problem from Concrete Abstractions
Your induction step is recorded incorrectly.

You wrote:

$$\frac{x^{k+1} - 1}{x - 1} + k+1$$

You should have written:

$$\frac{x^{k+1} - 1}{x - 1} + x^{k+1}$$

Basically, you are proving the formula for the sum of the geometric sequence.