How do you find the sum of the finite geometric sequence of #Sigma 2(-1/4)^n# from n=0 to 40?

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Roy E. Share
Mar 8, 2018

Answer:

#(8/5)*(1+(1/4)^41)#
#~=1.60000000...#

Explanation:

There are 41 terms in the series. The common ratio, #r# is #-(1/4)# and the first term, #a# is #2(-1/4)60# which is #2#. Therefore the sum of the first 41 terms is #a*(1-r^n)/(1-r)#
#=2*(1-(-1/4)^41)/(1-(-1/4))#
#=8/5*(1+(1/4)^41)# because 41 is odd
#~=1.6#
because #(1/4)^41# is negligible

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