Question 1173166
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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.<br>
{{{ sum(  (3 * 5^(n+1)/2^(2n)), n=8, 13) }}}<br>
Remove the factor of 3 and one of the factors of 5 in the numerator, and change {{{2^(2n)}}} in the denominator to {{{4^n}}}:<br>
{{{ 15*sum(  (5^n/4^n), n=8, 13) }}} = {{{ 15*sum(  (5/4)^n, n=8, 13) }}}<br>
Then<br>
{{{ 15*sum(  (5/4)^n, n=8, 13) }}} = {{{ 15*sum(  (5/4)^n, n=1, 13) -  15*sum(  (5/4)^n, n=1, 7) }}}<br>
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.<br>