Problem:

Find a formula for

a.

b. Also, show that if , then

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a. By the Geometric Sum Formula,

(1)

Since (2)

Let , then substitute r back into (1) yields

(3)

Before I simplify this fraction, this formula doesn't seem right to me.

Suppose n=2 and x=2, then the equation (2) becomes

However, if you plug n =2 and x = 2 into equation (3) , then it becomes

But

(b) Since

I'm unsure what I am doing incorrectly for part (a).

Thank you for your time.