Question 1118291
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Describe the series in words, instead of making us try to decipher your nonstandard symbols.<br>
The only possible logical interpretation I can see is the sum as n goes from 1 to 16 of {{{6(1/4)^n}}}.<br>
The infinite sum is (first term) divided by (1 minus the common ratio).  The first term is 6(1/4) = 3/2; the common ratio is 1/4:<br>
{{{S = (3/2)/(1-1/4) = (3/2)/(3/4) = (3/2)*(4/3) = 2}}}<br>
The terms after n=16 are tiny and will certainly bring the sum down only a tiny bit.<br>
So to the nearest whole number the sum of the finite geometric series is 2.