Series

AP Calculus AB/BC - Unit 10 Overview: Infinite Series and Sequences

Given a series ∑(n=1 to ∞) (1/n^3), what can be concluded about its convergence using the Integral Test?

If the integral ∫(1 to ∞) (x^2) dx is divergent, what can be concluded about the series ∑(n=1 to ∞) (n^2)?

If the integral ∫(1 to ∞) (1/x) dx is divergent, what can be concluded about the series ∑(n=1 to ∞) (1/n)?

What is the convergence behaviour of the series ∑(n=1 to ∞) (1/1+n) based on the Integral Test?

What is the convergence behavior of the series ∑(n=1 to ∞) 4/(n^2 +1) based on the Integral Test?

For the series ∑(n=1 to ∞) (1/n^(2)) what is the p-value of the series?

Which of the following can be used to compare a series with a p-series?

If a series is known to converge and a second series is less than or equal to it, what can we conclude about the convergence of the second series?

If the limit of the ratio between the terms of two series is equal to infinity, what can be concluded about their convergence?

Which of the following series can be said to converge based on the convergence of the series ∑(n=1 to ∞) (5/n^(2))?

Which of the following series can we use to determine the convergence behavior of the series ∑(n=1 to ∞) (ln(n)/n)?

Determine if the following series converge or diverge using the Ratio Test. ``` ∑ (2n)! / (3n + 10) ```

Determine if the following series converge or diverge using the Ratio Test. ``` ∑ ((4n-1)!) / (7n)! ```

Does the series $$\sum_{n=1}^{\infty} \frac{4n+3}{9n+1}$$ converge or diverge?

Which test should you use first when determining the convergence or divergence of a series?

If the series ∑(n=1 to ∞) ((-1)^(n)n/(n^3 -27)) converges absolutely, which of the following series must also converge?

If the series ∑(n=1 to ∞) ((-1)^n/n)) converges conditionally, which of the following series must also converge?

What is the convergence behavior of the series ∑(n=0 to infinity) (-1)^n/(n)?

What is the convergence behavior of the series ∑(n=0 to infinity) (-1)^n/(n^2)?