How do I find the sum of the infinite geometric series such that $a_1=-5$ and $r=1/6$ ?

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Answer 1 · 2015-05-23T22:03:39

For the infinite geometric series $S=a_1+a_1r+a_1r^2+cdots$ we can use the formula $S=a_1/(1-r)$ as long as $|r|<1$ .

In our case, $a_1=-5, r=1/6$ and $|r|=|1/6|=1/6<1$ so
$S=(-5)/(1-1/6)=(-5)/(5/6)=-5* 6/5=-6$

How do I find the sum of the infinite geometric series such that a_1=-5a_1=-5 and r=1/6r=1/6?