How do you find the sum of the infinite geometric series 5 + 5/3 + 5/9 + 5/27 +....?

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Answer 1 · 2015-12-26T15:01:30

The sum is #15/2#

You can rewrite this as follows

#5+5/3+5/9+5/27+...=5*(1+1/3+1/3^2+1/3^3+...)#

Now the sum #1+1/3+1/3^2+1/3^3+...# is given by the formula

#S=(a_1)/(1-r)#

where #a_1# is the first term of the series and #r# is the ratio of successive terms in our case #r=1/3#

Hence

#S=1/(1-1/3)=1/(2/3)=3/2#