Question

Can someone help solve these problems?
Write the series using sigma notation.
-9 + 3 -1 + 1/3 + ...

Answer 1

Each successive term is reduced by a factor of 3, so the common ratio is 1/3. The signs are also alternating, so you have (-1) to some power.
\[\sum_{n=0}^\infty9(-1)^{n+1}\left(\frac{1}{3}\right)^n\\
\sum_{n=0}^\infty-9\left(-\frac{1}{3}\right)^n\]