Question

evaluate the sum of the finite geometric series 1,3,9,27,...;n=8

Answer 1

You have the following sequence:

1 , 3 , 9 , 27 , ...

The last sequence can be written as follow:

$\sum ^{}_n3^n$

For n = 8, you obtain:

$\begin{gathered} \sum ^{}_n3^n=3^0+3^1+3^2+3^3+3^4+3^5+3^6+3^7+3^8 \\ \sum ^{}_n3^n=1+3+9+27+81+243+729+2187+6561 \\ \sum ^{}_n3^n=9841 \end{gathered}$

Hence, the sum is 9841