It seems like there might be some typos in the given series. Let's assume the series is:
$6(-2)^n + 5^{n+1}$ for $n=0, 1, 2, ...$
Now, we can rewrite this series as the sum of two geometric series:
$6(-2)^n + 5^{n+1} = 6\sum_{n=0}^{\infty}(-2)^n +
Show more…