Hello everybody, I am wondering how can I find the sum of the series ? I found out that the series converges for |z+i|>2, but I am not able to find the sum of the series , thank you very much

Printable View

- Jun 4th 2013, 11:39 AMalteraussum of the complex series
Hello everybody, I am wondering how can I find the sum of the series ? I found out that the series converges for |z+i|>2, but I am not able to find the sum of the series , thank you very much

- Jun 4th 2013, 12:25 PMHallsofIvyRe: sum of the complex series
If it weren't for that "n" at the beginning, that would be a geometric series. But that n makes me think of a derivative. If we set then . Does that give you any ideas?

- Jun 5th 2013, 12:43 AMalterausRe: sum of the complex series
Thanks for the reply ..

So you're saying that I could at first find the sum

and I get the function f(z)

and just count the derivative of f'(z) ?

this series looks not as difficult as the first one, but I still can't find the sum ..

would you please give me another hint? - Jun 5th 2013, 01:34 AMProve ItRe: sum of the complex series
- Jun 5th 2013, 02:05 AMalterausRe: sum of the complex series
okey,

can you please explain how does the geometric series work for complex numbers?

I dealt only with real geometric series and the sum is then easy

is there any sum formula for complex terms?

in my series number

thank you - Jun 9th 2013, 07:24 AMalterausRe: sum of the complex series
no more suggestions?

- Jun 9th 2013, 07:49 AMProve ItRe: sum of the complex series
It works exactly the same way as a real geometric series.

- Jun 9th 2013, 08:04 AMalterausRe: sum of the complex series
thank you very much, I found the result which looks to be right

- Jun 9th 2013, 07:31 PMSorobanRe: sum of the complex series
Hello, alteraus!

II found the sum.*think*

But check my work . . .*please!*

Quote:

I found out that the series converges for ,

but I am not able to find the sum of the series.

. . . . . . . . . .

The geometric series has first term and common ratio

. . Its sum is: .

We have: .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

- Jun 10th 2013, 12:53 AMalterausRe: sum of the complex series
Thank you very much Soroban,

nice way how to avoid the term-by-term differentiation,

by which I got the same sum of the series, so it looks to be right :)