Question

Find the sum of 3+9+27...+6561

Answer 1

The sum of the first n terms of a geometric series with first term a₁ and common ratio r is given by the formula
$S_{n}=a_{1}\cdot\dfrac{r^{n}-1}{r-1}$

Then your sum is
$\sum\limits_{n=1}^{8}3^{n}=3\cdot\dfrac{3^{8}-1}{3-1}=9840$

The sum of this geometric series with first term 3 and common ratio 3 is ...
   J  9840