I have this problem requiring me to show two infinite sums are equal but I can't seem to figure out how to do this. No matter what I try never give any results.
Hence my question is what approach should I use toward one of these question?
This is the question in question if it can help
Show
if |x|<1
Sorry, me again.
I also have the show a similar result for |x|>1
However using the power serie of
does not work in this case since it has as radius of convergence 1.
I must show if |x|>1 then
Unfortunately I am still as stuck and can't find a way to figure that one out even with the insight you gave me Olpag.
Anyone has an idea?
If you want a series that converges when |x| > 1 then you need it to use negative powers of x. So write (dividing top and bottom by ). You can then apply the previous result with in place of x, noticing that an extra minus sign will come in when you transform it back into positive powers of x.