What is the sum of the geometric series $Sigma 6(2)^n$ from n=1 to 10?

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Answer 1 · 2017-02-16T08:46:47

The sum is $12276$ . See explanation.

This expression can be written as:

$Sigma_{i=1}^10 (6xx2^n)=6xxSigma_{i=1}^10 2^n$

The last expression is a sum of a finite geometrical sequence for which: $a_1=2,q=2,n=10$ . This sum can be calculated as:

$S_10=2xx(1-2^10)/(1-2)=2xx(2^10-1)/(2-1)=2xx(2^10-1)=$

$=2xx1023=2046$

So the value of the first expression is: $6xx2046=12276$