# calculus

test the series for convergence or divergence

the series from n=0 to infinity of
(x^2+1)/(x^3+1)

I said that due to the limit comparison test this converges at 1

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1. <<the series from n=0 to infinity of
(x^2+1)/(x^3+1)>>

Where did the x come from? Shouldn't he variable be n?

For large n, it approaches the sum of 1/n with n going to infinity, which does NOT converge. You can prove that with the "integral test". It behaves like log n as n-> infinity

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