Worksheet: Integral Test for Series

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In this worksheet, we will practice using the integral test for series to determine whether a series containing nonnegative terms is convergent or divergent.

Q1:

Using the integral test, determine whether the series 12(2)+13(3)+14(4)+⋯lnlnln is convergent or divergent.

  • Adivergent
  • Bconvergent

Q2:

We will investigate the convergence or divergence of the series ∞1√2𝑛−1 using the integral test.

Evaluate 1√2𝑥−1𝑥∞d, if possible.

  • A0
  • B13
  • CThe integral diverges.
  • D1
  • E−13

Determine whether the series converges or diverges.

  • AIt diverges.
  • BIt converges.

Q3:

Determine whether the series ∞𝑛𝑒 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q4:

Use the integral test to determine whether the series ∞𝑛sin converges or diverges.

  • AThe series converges.
  • BThe series diverges.

Q5:

Determine whether the series ∞𝑒√𝑒+4 converges or diverges.

  • AThe series converges.
  • BThe series diverges.

Q6:

Use the integral test to determine whether the series ∞𝑛3+4𝑛 converges or diverges.

  • AThe series converges.
  • BThe series diverges.

Q7:

Determine whether the series ∞𝑛𝑛+1tan converges or diverges.

  • AThe series converges.
  • BThe series diverges.

Q8:

Use the integral test to determine whether the series ∞1𝑛 converges or diverges.

  • AThe series converges.
  • BThe series diverges.

Q9:

Determine whether the series ∞𝑒 converges or diverges.

  • AThe series converges.
  • BThe series diverges.

Q10:

Determine whether the series ∞√𝑛𝑛ln converges or diverges.

  • AThe series diverges.
  • BThe series converges.

Q11:

Use the integral test to determine whether the series ∞𝑒 is convergent or divergent.

  • ADivergent
  • BConvergent

Q12:

Use the integral test to determine whether the series ∞1𝑛 is convergent or divergent.

  • ADivergent
  • BConvergent

Q13:

Use the integral test to determine whether the series ∞(𝑛)𝑛ln is convergent or divergent.

  • ADivergent
  • BConvergent

Q14:

Use the integral test to determine whether the series ∞1(3𝑛+7) is convergent or divergent.

  • AConvergent
  • BDivergent

Q15:

Use the integral test to determine whether the series ∞2𝑛+13𝑛+3𝑛+1 is convergent or divergent.

  • ADivergent
  • BConvergent

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