How do you find the sum of the infinite geometric series 2 + 1.5 + 1.125 + 0.8437 +…?

1 Answer
Alan P.
Jan 20, 2016

#2+1.5+1.125+0.84375+ ... = 8#

Explanation:

The sum of an infinite geometric series with initial value #a_1# and ratio #r, abs(r) < 1# is given by the formula:
#color(white)("XXX")Sigma a_i = a_1/(1-r)#

Since for the given series:
#color(white)("XXX")1.5/2 = 1.125/1.5 = 0.84375/1.125 = 0.75#
#r=0.75#

and
#color(white)("XXX")Sigma a_i = 2/(1-0.75) = 8#

Note: since we were told this was a geometric series I felt justified in replacing #0.8437# with #0.84375#

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