ChalkBee

Alternating Series & Absolute vs Conditional Convergence (Calculus II)

Free printable university Calculus II worksheet on alternating series: the alternating series test, and deciding between absolute convergence, conditional convergence and divergence.

✓ Answer key checked by math, never wrong
Calculus II · Math worksheet
Name
Date
Math

Calculus II: Alternating Series & Absolute vs Conditional Convergence

First check whether the terms approach 0 (if not, the series diverges). Then apply the alternating series test, and finally test Σ |aₙ| to decide between absolute and conditional convergence.

  1. 1.
    Determine whether the series Σ[n=1 to ∞] (1)n+1(-1)^{n+1}/n3n^{3} converges absolutely, converges conditionally, or diverges.
  2. 2.
    Determine whether the series Σ[n=1 to ∞] (1)n+1(-1)^{n+1}/n2n^{2} converges absolutely, converges conditionally, or diverges.
  3. 3.
    Determine whether the series Σ[n=1 to ∞] (1)n+1(-1)^{n+1}/n converges absolutely, converges conditionally, or diverges.
  4. 4.
    Determine whether the series Σ[n=1 to ∞] (1)n+1(-1)^{n+1}/√n converges absolutely, converges conditionally, or diverges.
  5. 5.
    Determine whether the series Σ[n=1 to ∞] (1)n+1(-1)^{n+1}/(2n + 6) converges absolutely, converges conditionally, or diverges.
  6. 6.
    Determine whether the series Σ[n=1 to ∞] (1)n+1(-1)^{n+1}/(5n + 4) converges absolutely, converges conditionally, or diverges.
  7. 7.
    Determine whether the series Σ[n=1 to ∞] (1)n+1(-1)^{n+1}·n/(2n + 1) converges absolutely, converges conditionally, or diverges.
  8. 8.
    Determine whether the series Σ[n=1 to ∞] (1)n+1(-1)^{n+1}·n/(3n + 5) converges absolutely, converges conditionally, or diverges.
Made with ChalkBee · chalkbee.com

More like this

Other Calculus II worksheets