Question

How do you find the sum of the infinite series `Sigma7(1/10)^k` from k=1 to `oo`?

Answer 1

`7/9`

Explanation:

This is equal to `7 sum_1^oo 1/10^k`

This is now a geometric series with first term `1/10` and common ratio `1/10` or say, both are 0.1

Therefore, the sum of this series would be `7 0.1/(1-0.1)`
[formula for sum of an infinite geometric series is `a/(1-r), where, r<1`)

`(7(0.1))/0.9 = 7/9`