- #1

ReidMerrill

- 68

- 2

## Homework Statement

Find all values of x such that the given series would converge

Σ6

^{n}(x-5)

^{n}(n+1)/(n+11)

## Homework Equations

## The Attempt at a Solution

By doing the ratio test I found that

lim 6

^{n}(x-5)

^{n}(n+1)/(n+11) * (n+12)/[6

^{n+1}(x-5)

^{n+1}(n+2)]

n→inf

equals 1/(6(x-5)) * lim (n+12)(n+1)/(n+11)(n+2)

This limit = 1 so to solve for the x I set

-1<1/6(x-5) and 1/6(x-5)<1 and found the (31/6)<x<(29/6)

but apparently this is incorrect. What am I doing wrong?