Question

What is 1+a+a^2+a^3+a^4........ ?

Answer 1

See explanation.

Explanation:

The question says about the sum of a geometric sequence with:

`a_1=1` and `q=a`

A geometric sequence is:

• convergent if `-1 < q < 1`

• divergent if `|q| >=1`

So the sum is finite only if `-1< a < 1` and then the sum is:

`S=1/(1-a)`