Question

Question #83975

Answer 1

Geometric Series

`a+ar+ar^2+ cdots = a/{1-r}" "` if `" "-1 < r < 1`

---

Since

`b(1+b+b^2+ cdots)=b+b^2+b^3+ cdots`

is a geometric series with `{(a=b),(r=b):}`, its sum `S` can be found by

`S=b/{1-b}" "` if `" "-1 < b < 1`.

For other values of `b`, the series diverges.

---

I hope that this was helpful.