Question

How do you find the sum of the infinite geometric series 1+0.1+0.01...?

Answer 1

`1 1/9`

Explanation:

I'm guessing here you are talking about the limiting sum...

SO the limiting sum = `a/(1-r)`
where a is your first number which in this case is 1 and r is the ratio between two terms

however your ratio has a `absr < 1` for your limiting sum to work

In your case, `r=0.1/1 = 0.1`

Therefore, your limiting sum is `1/(1-0.1)=1 1/9`