# Thread: [SOLVED] need a urgent help in sum of series

1. ## [SOLVED] need a urgent help in sum of series

Hi.
can anyone give me a complete solutions to the problem below..
Need urgently

Find The sum of series of,
$
cos(3x) + \sum_{n=1}^{\infty}\frac{(-1)^n cos^3(3^nx)}{3^n}
$

Need an urgent help to solve these kind of series problem..I need the full solution part

2. Originally Posted by saggi_twist
Hi.
can anyone give me a complete solutions to the problem below..
Need urgently

Find the sum of series
Cos3x –((1/3)*( Cos(3x)*Cos(3x)*Cos(3x))+((1/9)* Cos(9x)*Cos(9x)* Cos(9x)) – ((1/27)*Cos(27x)*Cos(27x)*Cos(27x))+…..

Need an urgent help to solve these kind of series problem..
Can't you try to give this to us in a clearer manner? That is a very messy series. It's nearly impossible to figure out.

3. Originally Posted by janvdl
Can't you try to give this to us in a clearer manner? That is a very messy series. It's nearly impossible to figure out.
$cos(3x) + \sum_{n=1}^{\infty}\frac{(-1)^n cos^3(3^nx)}{3^n}$

4. I think it's
$Cos(3x)-\frac{1}{3} Cos(3x)^3+\frac{1}{9} Cos(9x)^3-\frac{1}{27} Cos(27x)^3+\frac{1}{81} Cos(81x)^3\text{...}
$

Which can be shown in sum notation,

$Cos(3x) + \sum_{n=1}^{\infty}(-\frac{1}{3})^n Cos^3(3^{n}x)$

5. Is there a summation formula for, $\sum_{n=0}^{\infty} \frac{(-1)^n x^{3^n}}{3^n} ~ |x|\leq 1$?
I was able to reduce your sum to that sum.