sum of the first n terms of the following sequence....

[leilsilver]

What is the sum of the first n terms of the following sequence? 1, (1+3), (1+3+3^2), (1+3+3^2+3^3),....?

I have no idea where to go with his other than knowing it's sa form of summation notation.

 

[pka]

This may get you started.
\(\displaystyle \L
\begin{array}{l}
{1 } \\
{1 + 3 } \\
{1 + 3 + 3^2 } \\
{1 + 3 + 3^2 + 3^3 } \\
\vdots \\
{1 + 3 + 3^2 + 3^3 \cdots + 3^{n - 1} } \\
\hline
{n + (n - 1)3 + (n - 2)3^2 + (n - 3)3^3 \cdots + (1)3^{n - 1} } \\
\end{array}\).

Written as a sum: \(\displaystyle \L
\sum\limits_{k = 0}^{n - 1} {(n - k)\left( {3^k } \right)}\)