# Find the sum of series

1. Sep 8, 2006

### vin-math

Can anyone teach me how to find the sum of the series in terms of n in the following:

1+2x3^2+3x3^4+............+(n+1)3^2n

Thx!

2. Sep 8, 2006

### 0rthodontist

This can be done with generating functions if you know them.
1. Find the generating function for 1, 3^2, 3^4, ...
2. From this, find the generating function for 1, 2*3^2, ...
3. Find the generating function for (n+2)*3^(2(n+1)), (n+3)*3^(2(n+2)), ...
4. Subtract the latter from the former and evaluate at 1.

3. Sep 8, 2006

### vin-math

i dont know what generating function is but what i know is to use the summation sign to do this kind of question. i still cant do it.........

4. Sep 8, 2006

### shmoe

You might find it easier to try and sum:

$$1+2x^2+3x^4+\ldots+(n+1)x^{2n}$$

5. Sep 8, 2006

### shmoe

You might find it easier to try and sum:

$$1+2x^2+3x^4+\ldots+(n+1)x^{2n}$$

It's not quite a geometric series, but can you turn it into one?

6. Sep 8, 2006

### 0rthodontist

Okay--what sums can you do that might be relevant?

7. Sep 8, 2006

### vin-math

i just can do till this step:

n+1 E(Sigma) r=1 (r*x^(r-1))

8. Sep 8, 2006

### vin-math

I can do the summation of x, x^2 .....x^n, x(x+1),x(x+1)(x+2).....

actually this is my first time to touch this kind of math:)

9. Sep 8, 2006

### 0rthodontist

Well--
x + x^2 + ... + x^n
Take the derivative with respect to x, both term-by-term and in the sum you know.

Last edited: Sep 8, 2006