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#