Question

Find S∞ (if it exists)?
100-10+1-1/10+...

Answer 1

\[\sum_{0}^{\infty}(10)^{-n}*(-1)^n\]

Answer 2

\[\sum_{0}^{\infty}(((10))^{-1})^{n} * (-1)\]
\[\sum_{0}^{\infty}({1 \over 10})^{n} * (-1)^{n}\]
\[\sum_{0}^{\infty}({-1 \over 10})^{n} \]

Answer 3

It is a geometric series

Answer 4

so we use its formula
1/(1-r)
1/(1-(-1/10))
1/(1+1/10)

Answer 5

1/(11/10)
10/11

Answer 6

http://www.wolframalpha.com/input/?i=Sum%5B%28%28-1%2F10%29^n%29%5D