Hi everyone,
I am struck in an expansion. Hope someone could help me in this expansion.
The expansion that I have is
1+(2^2)(r^2)+(3^2)(r^4)+(4^2)(r^6)+....... , 1+(2^4)(r^2)+(3^4)(r^4)+(4^4)(r^6)+....... , ......
Can we find geometric progression for this expansion.
Thank you .....
I tried to find the solution for 2nd part in the same way. I tried many iterations but I could not find something that can be taken common(as 2r^2 in the above proof) to make in to geometric series.
The problem is that I have many series like this (2^2, 2^4, 2^6,.....). Can we generalize the solution.
Thanks in advance
That was a beautiful piece of manipulation. I was admiring it so closely that I found a small transcription error. Small point, but, just in case anyone else is following closely (they should!):
In the 2nd and 3rd lines of the quote, the appearance of were obviously intended to be .
You corrected it by the final equals expresssion on the 3rd line of the quote.