document.write( "Question 1173166: What is the sum of $\"+sum%28++%283+%2A+5%5E%28n%2B1%29%2F2%5E%282n%29%29%2C+n=8%2C+13%29+\"$ ? \n" ); document.write( "

Algebra.Com's Answer #798353 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "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.

\n" ); document.write( " $\"+sum%28++%283+%2A+5%5E%28n%2B1%29%2F2%5E%282n%29%29%2C+n=8%2C+13%29+\"$

\n" ); document.write( "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 $\"4%5En\"$ :

\n" ); document.write( " $\"+15%2Asum%28++%285%5En%2F4%5En%29%2C+n=8%2C+13%29+\"$ = $\"+15%2Asum%28++%285%2F4%29%5En%2C+n=8%2C+13%29+\"$

\n" ); document.write( "Then

\n" ); document.write( " $\"+15%2Asum%28++%285%2F4%29%5En%2C+n=8%2C+13%29+\"$ =

\n" ); document.write( "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.

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