How do you find the sum of the finite geometric sequence of #Sigma 8(-1/2)^i# from i=0 to 25?

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Answer 1 · 2017-12-09T11:37:33

See below.

The sum of a geometric series is given by:

#a((1-r^n)/(1-r))#

Where #a# is the first term, #r# is the common ratio and #n# is the nth term.

For #i=0# the first term is:

#8(-1/2)^i=8(-1/2)^0=8(1)=8#

Common ratio is #-1/2#

#:.#

#8((1-(-1/2)^25)/(1-(-1/2)))=8((1-(-1/32^5))/(3/2))#

#=((16+(16/32^5))/3)=5.333333254#