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.

  • A 1 3
  • B − 1 3
  • C1
  • DThe integral diverges.
  • E0

Determine whether the series converges or diverges.

  • AIt converges.
  • BIt diverges.

Q3:

Determine whether the series ∞𝑛𝑒 converges or diverges.

  • AIt converges.
  • BIt diverges.

Q4:

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

  • AThe series diverges.
  • BThe series converges.

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 diverges.
  • BThe series converges.

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.

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