Question

Find the values of x for which the series converges. Find the sum of the series for those values of x.

Answer 1

\[\sum_{n=1}^{\infty} (x+2)^n\]

Answer 2

@ganeshie8

Answer 3

x<3 is my first guess

Answer 4

You love your x?

Answer 5

An infinite series converges when the last term approaches zero.

Answer 6

lol, was this a trick question?

Answer 7

Nope

Answer 8

x < 3?

x = 2 doesn't seem to work.

Answer 9

What's the common ratio?

Answer 10

Well, I'd say that\[-1 < x+2 < 1\]

Answer 11

That's right

Answer 12

thats not how u solve it, its a geometric series with some shift

Answer 13

that's the interval of convergence

Answer 14

x+2 is the ratio

Answer 15

let y=x+2
sum of n from 1 to inf of y^n

Answer 16

Yeah, so |r|=|x+2|<1 is when it converges

Answer 17

Great.

For the series to converge, you want the common ratio's abs value to be less than 1.

Answer 18

Yeah.

Answer 19

And\[S = \dfrac{a}{1-r} = \dfrac{x+2}{1 - x - 2}\]

Answer 20

Yup