Question

find interval of convergence for the given series (screenshot included)

Answer 1

Have you considered the Ratio Test?

Answer 2

for some reason when I use the ratio test I end up with lim of (n+1), which is infinity

Answer 3

1) Where did the (x-1) go?
2) What does that tell us?

Answer 4

it's pulled out infront of the limit, right? So then you would have infinity multiplied with it

Answer 5

@tkhunny

Answer 6

1) You don't "have" infinity. "infinity" isn't anything. What you have is an unbounded expression.

2) How can you get an unbounded expression to behave itself?

Answer 7

I'm not sure... I don't remember going over any examples like this in class at all. :(

Answer 8

We have an unbounded expression.

If we multiply it by 6, will it behave itself?
If we multiply it by 3, will it behave itself?
If we multiply it by 1, will it behave itself?
If we multiply it by -2, will it behave itself?

Answer 9

does this mean it will converge if it's less than 2?

Answer 10

I'm sorry I don't follow. I'm sorry :( I'll just give you best answer anyway

Answer 11

?? No, it's still unbounded. There is only ONE value that will get the unbounded expression under control. Square root of two? pi? What magic number will do the trick?

Answer 12

Try x = 1. What happens?