Question

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

Answer 1

So the series looks something like this:

`\Sigma_(n=4)^(\infty)(n-1)/(16) \\</p><p>(1)/(16)\Sigma_(n=4)^(\infty)n-1`

If
`\lim_(n\rightarrow\infty)\\eq` 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