Question

Evaluate the infinite series

Answer 1

A.

24

B.
-4/3

C.
-8/5

D.

It does not have a sum.

Answer 2

the series diverge

Answer 3

im not so sure what ya mean there?

Answer 4

it means that the larger \(n\) gets the larger \(6^n\) gets so you cannot add up an infinite number of larger and larger numbers and get a finite answer

Answer 5

its going to be a fraction right?

Answer 6

not only do the terms have to get smaller and smaller, they have to get smaller very fast f

Answer 7

oh no

Answer 8

it is not a fraction, it does not exist

Answer 9

So that means that it will not have a sum ?

Answer 10

imagine trying to add \(5+5+5+...\) it is too large to add up forever

Answer 11

yes, it will not have a sum

Answer 12

oh okay, i understand now

Answer 13

you can only add up an infinite number of numbers if they get small quickly
like for example
\[1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...\]

Answer 14

your numbers get larger and larger not smaller