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

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