# Finding x in a geometric progression, given the sum.

1. Sep 14, 2010

### NotaPhysicist

1. The problem statement, all variables and given/known data

If

$$1 + 2x + 4x^2 + ... = \frac{3}{4}$$

find the value of x. [Edit: Forgot to ask the question]

2. Relevant equations

$$S_n = \frac{a(1 - r^n)}{1 - r}$$

$$t_n = ar^{n-1}$$

3. The attempt at a solution

a = 1

r = 2x

I try to solve $$S_n$$ and end up with

$$2x^n = \frac{6x - 7}{4}$$

which I can't solve.

I try to solve by equating t2 and t3 and getting x = (1/2). Which is wrong.

Any help appreciated.

Last edited: Sep 15, 2010
2. Sep 14, 2010

### zorro

Is the sum is to infinity?
or to 'n terms'?

If it is to infinity, Apply limit to your equation.

3. Sep 14, 2010

### HallsofIvy

If this is an infinite sum the formula is
$$S_\infty= \frac{a}{1- r}$$

If it is a finite sum, you would need to know how many terms so that "n" would be an actual integer, not a variable.

The "..." at the end of the sum indicates it is an infinite sum.

4. Sep 15, 2010

### NotaPhysicist

I've edited the original post. The problem is to find the value of x.

Its not an infinite sum. The only solution I can see is to solve for n in the infinite series and the summation, and try to solve simultaneously.

5. Sep 15, 2010

### NotaPhysicist

I had to read your answer a couple of times. I get it now. Its an infinite sum. No powers to work out.

Thank you so much.