Question

Find the sum of the infinite geometric series, if it exists.

Answer 1

So the series looks something like this:

$\Sigma_{n=4}^{\infty}\frac{n-1}{16} \\\frac{1}{16}\Sigma_{n=4}^{\infty}n-1$

If $\lim_{n\rightarrow\infty}\neq$ than $\Sigma{a_n}$ diverges. So we must apply limit infinity property:

$\lim_{n\rightarrow\infty}(ax^n+\dots+bx+c)=\infty, a>0$ and n is odd.

So...

$\lim_{n\rightarrow\infty}n-1=\infty$

The series diverges.

Hope this helps.

r3t40