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

4 - 1 + 1/4 - 1/16 + . . .

a. -1

b. 16/5

c. 3

d. does not exist

Respuesta :

r3t40

So the series looks something like this:

[tex]\Sigma_{n=4}^{\infty}\frac{n-1}{16} \\

\frac{1}{16}\Sigma_{n=4}^{\infty}n-1[/tex]

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

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

So...

[tex]\lim_{n\rightarrow\infty}n-1=\infty[/tex]

The series diverges.

Hope this helps.

r3t40