Answer
$\approx 1409.83544$
Work Step by Step
We are given the geometric sum:
$\sum_{k=0}^6 \pi^k$
$S_7=a+ar+...+ar^6=\sum_{k=0}^6 ar^k=a\dfrac{1-r^7}{1-r}$
The geometric sequence has the ratio $r=\pi$ and the first term $a=1$.
Compute the sum:
$S_7=\sum_{k=0}^6 \pi^k=1\dfrac{1-\pi^7}{1-\pi}\approx 1409.83544$
