SOLUTION: What is the sum of {{{ sum( (3 * 5^(n+1)/2^(2n)), n=8, 13) }}}?

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Question 1173166: What is the sum of +sum%28++%283+%2A+5%5E%28n%2B1%29%2F2%5E%282n%29%29%2C+n=8%2C+13%29+?
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


One way to get the answer would be to convert the given sum to a purely geometric series and use the formula for the sum of a finite geometric series.

+sum%28++%283+%2A+5%5E%28n%2B1%29%2F2%5E%282n%29%29%2C+n=8%2C+13%29+

Remove the factor of 3 and one of the factors of 5 in the numerator, and change 2%5E%282n%29 in the denominator to 4%5En:

+15%2Asum%28++%285%5En%2F4%5En%29%2C+n=8%2C+13%29+ = +15%2Asum%28++%285%2F4%29%5En%2C+n=8%2C+13%29+

Then

+15%2Asum%28++%285%2F4%29%5En%2C+n=8%2C+13%29+ =

But the formula for the sum of a finite geometric series is awkward to use -- so you might as well simply evaluate the given sum directly, possible using an excel spreadsheet.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


Wolframalpha gives the exact answer



67552734375%2F67108864



Edwin