# 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

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

posted by drwls

## Similar Questions

1. ### calculus

test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (-1)^n/(3n+1) I said it converges, is this true?
2. ### calculus

test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (-1)^n/(3n+1) I said it converges, is this true?
3. ### Calculus

If you have a geometric alternating series, and you prove that the series is converging by doing geometric series test, and NOT alternating series test, then does that allow you to say that the series converges ABSOLUTELY? Or
4. ### Calc

Does 1/ln(x+1) converge or diverge? I've tried the nth term test, limit comparison test, and integral test. All I get is inconclusive. The other tests I have (geometric series, p-series, telescoping series, alternating series, and
5. ### math

test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (-1)^n/(3n+1) I said it converges, is this true?
6. ### calculus

test the series for convergence or divergence. the sum from n=1 to infinity of ((-1)^n*e^n)/(n^3) I said it converges because the derivative of (1/n^3) is decreasing
7. ### calculus

Consider ∞ ∑ [(3k+5)/(k²-2k)]ᵖ, for each p ∈ ℝ. k=3 Show this series { converges if p > 1 { diverges if p ≤ 1 Hint: Determine the known series whose terms past the second give an approximate
8. ### calculus

test the series for convergence or divergence. the sum from n=1 to infinity of ((-1)^n*e^n)/(n^3) I said it converges because the derivative of (1/n^3) is decreasing is this true?
9. ### Calculus

I'm studying infinite series and am really struggling with memorizing all the tests for convergence in my book, there's like 10 of them. I don't think I'm going to be successful in memorizing all of them. I will never be asked in
10. ### Calc II

Use the comparison or limit comparison test to decide if the following series converge. Series from n=1 to infinity of (4-sin n) / ((n^2)+1) and the series from n=1 to infinity of (4-sin n) / ((2^n) +1). For each series which

More Similar Questions