# Not able to simplify this summation formula?

1. Jan 10, 2014

### musicgold

Hi,

Please see the attached pdf file. Equation 1 and equation 2 are equivalent.

Thanks.

#### Attached Files:

• ###### summation formula.pdf
File size:
24 KB
Views:
103
Last edited: Jan 10, 2014
2. Jan 10, 2014

### Mentallic

The summation variable is n, so x can be considered a constant hence it can be pulled out the front.

What is

$$1+r+r^2+...+r^n$$

equal to?

3. Jan 10, 2014

### musicgold

Please see the new attached file.
This is how far I could go.

#### Attached Files:

• ###### summation formula 2.pdf
File size:
48.5 KB
Views:
86
4. Jan 10, 2014

### HallsofIvy

Staff Emeritus
The point is that both of your series are geometric series. What you do in your last post is essentially repeating the proof that the sum of the geometric series, $\sum_{n=0}^\infty r^n$ is $\frac{1}{1- r}$ except that you have $r= \frac{1}{\gamma}$.

5. Jan 10, 2014

### Mentallic

There is no mention of infinite sums.

musicgold, so what is

$$\sum_{i=1}^{n}\frac{1}{1+y}$$

And hence, let n=10. Also,

$$\frac{1-\frac{1}{\gamma^{n+1}}}{1-\frac{1}{\gamma}}$$

Can be simplified further. At least get rid of the fraction within the denominator.

6. Jan 10, 2014

### musicgold

I think, I am close, but not sure how to get rid of the 'y' in the encircled term.
What am I missing?

#### Attached Files:

• ###### summation 3.pdf
File size:
47.8 KB
Views:
80
7. Jan 10, 2014

### Mentallic

Sorry, this was supposed to be

$$\sum_{i=1}^{n}\frac{1}{(1+y)^i}$$

We're looking for

$$\sum_{n=1}^{10}\frac{1}{(1+y)^n}$$

while you're finding

$$\sum_{n=0}^{10}\frac{1}{(1+y)^n}$$

In your second attachment when you found

$$s=\sum\frac{1}{\gamma^n}=1+\frac{1}{\gamma}+\frac{1}{\gamma^2}+...$$

You began the sum with n=0 when you should've began with n=1.

8. Jan 15, 2014

### musicgold

Mentallic,

Yes. I was able to solve it with that correction. See attached. Thank you very much.

#### Attached Files:

• ###### summation 4.pdf
File size:
36.8 KB
Views:
80
9. Jan 16, 2014

Good work