Question

Find the interval of convergence for http://puu.sh/fHPxD/1dc316740d.png

Answer 1

i got ]1, 19[ but it says not correct

Answer 2

Checking with the ratio test,
\[\lim_{n\to\infty}\left|\frac{(x-10)^{n+1}}{(n+1)(-9)^{n+1}}\times\frac{n(-9)^n}{(x-10)^n}\right|=9|x-10|\lim_{n\to\infty}\frac{n}{n+1}=9|x-10|\]
The series will converge for \(9|x-10|<1\).

Answer 3

wait but (-9)^n/(-9)^(n+1) = 1/9

Answer 4

Ah sorry, minor typos can make big mistakes... Right, the 9 should be inverted to 1/9.

Answer 5

Your endpoints for the interval are correct, but keep in mind that the ratio test succeeds if the limit is STRICTLY less than 1, not less than or equal to.

Answer 6

wait but how the F it says this is incorrect http://puu.sh/fHQTR/945fa97277.png

Answer 7

Online homework assignments can be dumb like that... Your answer is right.

Answer check: http://www.wolframalpha.com/input/?i=Sum%5B%28x-10%29%5En%2F%28n+%28-9%29%5En%29%2C%7Bn%2C1%2CInfinity%7D%5D

Answer 8

thanks bro