Question

Find the values of x for which the series converges: ((summation)(n=1 to infinity)) (x-1)^n/3^n

Answer 1

lim of an/a(n-1)

as n goes inf

Answer 2

\[\lim \frac{(x-1)^n}{3^n}\frac{3^{n-1}}{(x-1)^{n-1}}\]
\[\lim \frac{(x-1)}{3}\]
\[|\frac{x-1}{3}|\lim 1\]

Answer 3

I thought it was n+1??

Answer 4

\[|\frac{x-1}{3}|<1\]
\[|x-1|<3\]

-2 < x < 4

Answer 5

its simply next/now

how you wanna represent that is up to you

Answer 6

Thanks!! I understand

Answer 7

yw :)