SOLUTION: Show that in any GP, S(2n): S(n)=(r^n+1):1 Thanks!

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Question 826711: Show that in any GP, S(2n): S(n)=(r^n+1):1
Thanks!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Show that in any GP,
S%5B2n%5D%22%3A%22S%5Bn%5D%22%22=%22%22r%5En%2B1%22%3A%221 
S%5Bn%5D%22%22=%22%22a%5B1%5D%281-r%5En%29%2F%281-r%29

So

S%5B2n%5D%22%22=%22%22a%5B1%5D%281-r%5E%282n%29%29%2F%281-r%29

-------------------------------------------------

S%5B2n%5D%2FS%5Bn%5D%22%22=%22%22%28a%5B1%5D%281-r%5E%282n%29%29%2F%281-r%29%29%2F%28a%5B1%5D%281-r%5En%29%2F%281-r%29%29%22%22=%22%22a%5B1%5D%281-r%5E%282n%29%29%2F%281-r%29%22%F7%22a%5B1%5D%281-r%5En%29%2F%281-r%29%22%22=%22%22a%5B1%5D%281-r%5E%282n%29%29%2F%281-r%29%22%22%2A%22%22%281-r%29%2Fa%5B1%5D%281-r%5En%29%22%22=%22%22
cross%28a%5B1%5D%29%281-r%5E%282n%29%29%2F%28cross%281-r%29%29%22%22%2A%22%22%28cross%281-r%29%29%2Fcross%28a%5B1%5D%29%281-r%5En%29%22%22=%22%22%281-r%5E%282n%29%29%2F%281-r%5En%29%22%22=%22%22%28%281-r%5En%29%281%2Br%5En%29%29%2F%281-r%5En%29%22%22=%22%22%28%28cross%281-r%5En%29%29%281%2Br%5En%29%29%2F%28cross%281-r%5En%29%29%22%22=%22%22
1%2Br%5En%22%22=%22%22%28r%5En%2B1%29%2F1

S%5B2n%5D%2FS%5Bn%5D%22%22=%22%22%28r%5En%2B1%29%2F1

is equivalent to the proportion:

S%5B2n%5D%22%3A%22S%5Bn%5D%22%22=%22%22r%5En%2B1%22%3A%221 

Edwin