Question

Find a geometric series with the sum of 4. Explain your process.

Answer 1

Infinite or finite?
\[\sum_{n=0}^\infty ar^n=\frac{a}{1-r}\quad\text{if }|r|<1\]while
\[\sum_{n=0}^k ar^n=\begin{cases}\dfrac{a(1-r^{k+1})}{1-r}&\text{for }r\neq1\\[1ex]k+1&\text{for }r=1\end{cases}\]