Find the interval and ratio of convergence for this series
sum of (-1)^n (n^2)(x^n)/ 4^n
n = 2 to infinity
Honestly, I'm totally lost. I know a ratio test has to be in there somewhere but I have no clue.
Help please!
sum of (-1)^n (n^2)(x^n)/ 4^n
n = 2 to infinity
Honestly, I'm totally lost. I know a ratio test has to be in there somewhere but I have no clue.
Help please!
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If you know how to do the ratio test its lim n goes to infinity of absolute value(a^n+1)/a^n
When you cross everything out you get x/4((n+1)/n)^2 so you get -1
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When you cross everything out you get x/4((n+1)/n)^2 so you get -1
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The ratio is the formula i mentioned above with the a's it will look like:lim (((-1)^n+1*(n+1)^2(x^(n+1))/4^… (-1)^n (n^2)(x^n)/ 4^n) Kinda hard to type out on the computer but if you can see it the n's cancel and simplify you can write it over each other but i prefer that way. Hope that helps.
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