Who solve this step by step $$s=1+3x+5x^{2}+7x^{3}+...$$

Question

anonymous · Answer

First term is looking like Arithmetic Progression and Second one is like Geometric Progression..

anonymous · Answer

yape

hartnn · Answer

sum of infinite arithmetico-geometric series...

anonymous · Answer

Sum of odd numbers to infinite we have to find first..

anonymous · Answer

Oh @hartnn you have made by work easy by writing that..

anonymous · Answer

Since @hartnn loves AP GP etc hartnn will solve this..

hartnn · Answer

let me search the formula...

anonymous · Answer

I will give you the answer after 5 min until then solve it

anonymous · Answer

I think it will not take the time when the speed is atleast 11Mbps @hartnn

anonymous · Answer

How I did was like this:
1+3x+5x^2+7x^3+9x^4+...
1+x+2x+x+4x^2+x^3+6x^3+x^4+8x^4+...
(1+x+x^2+x^3+x^4+...) (2x+4x^2+6x^3+8x^4+...)

hartnn · Answer

i just woke up, atleast let me open my eyes.....

anonymous · Answer

not that way @sauravshakya

anonymous · Answer

ok 5 more min @hartnn

anonymous · Answer

The second bracket will again contain the same @sauravshakya

anonymous · Answer

(1+x+x^2+x^3+x^4+...) 2* (x+2x^2+3x^3+4x^4+...)

hartnn · Answer

(1-3x)/(x-1)^2    ??

anonymous · Answer

nope @hartnn

anonymous · Answer

Now, the first sereies of first box will contain n terms and series of second box will contain n-1 terms

hartnn · Answer

was i even close to answer ?

anonymous · Answer

For second box series:|dw:1348305725661:dw|