Question

How do you find the sum of the infinite geometric series `4(1/3)^(n - 1)`?

Answer 1

`sum_(n=1)^oo4(1/3)^(n-1)=3/2`

Explanation:

Any geometric series of the form `sum_(n=1)^ooar^(n-1)` converges to the value `a/(1-r)` provided `|r|<1`.

In this case, `a=4 and r=1/3<1`.

Hence the sum of the series converges to `4/(1-1/3)=3/2`.