Worksheet: Power Series and Radius of Convergence

In this worksheet, we will practice defining a power series and finding the radius of convergence of the power series.

Q1:

Find the interval of convergence for the power series 𝑥5𝑛+10.

  • A[1,1)
  • B(1,1]
  • C(1,1)
  • D(0,1)
  • E[0,1)

Q2:

Find the interval of convergence of the power series 5𝑥3.

  • A2725,2725
  • B2725,2725
  • C35,35
  • D35,35
  • E(,)

Q3:

Determine the interval of convergence of the series (2𝑥+5)(𝑛+1)3.

  • A[4,1]
  • B12,12
  • C(4,1)
  • D32,32
  • E32,32

Q4:

Consider the power series (1)(2𝑥+9)𝑛+6.

Find the interval of convergence of the power series.

  • A[5,4]
  • B[5,4)
  • C(4,5)
  • D(5,4)
  • E(5,4]

Find the radius of convergence of the power series.

Q5:

Find the radius of convergence for the power series (𝑛1)!(𝑥5)𝑛.

Q6:

Consider the power series (3𝑥)𝑛+5.

Find the interval of convergence of the power series.

  • A13,13
  • B(,)
  • C13,13
  • D(1,1)
  • E13,13

Find the radius of convergence of the power series.

  • A13
  • B0
  • C23
  • D
  • E1

Q7:

Find the interval of convergence for the power series (𝑥2)𝑛!.

  • A(,)
  • B[1,3)
  • C(1,1)
  • D(1,3)
  • E[1,1)

Q8:

Consider the power series 𝑛(2𝑥).

Determine the radius of convergence of the power series.

  • A2
  • B
  • C12
  • D0
  • E1

Determine the interval of convergence of the power series.

  • A12,12
  • B12,12
  • C(,)
  • DThe series converges only at 𝑥=0
  • E12,12

Q9:

Consider the power series 𝑥(4𝑛+3).

Determine the interval of convergence of the power series.

  • A[1,1)
  • B14,14
  • C[1,1]
  • D(1,1)
  • E14,14

Determine the radius of convergence of the power series.

Q10:

Consider the power series (1)(3𝑥+4)𝑛.

Determine the radius of convergence of the power series.

  • A
  • B1
  • C0
  • D13
  • E23

Determine the interval of convergence of the power series.

  • A(5,3)
  • B53,1
  • C53,1
  • D(,)
  • E[5,3]

Q11:

Find the interval of convergence of the power series (𝑥+3)6𝑛.

  • A(2,4)
  • B[4,2)
  • C(4,2)
  • D[4,2]
  • E[2,4)

Q12:

Find the radius of convergence of the power series (2)𝑛+3(𝑥+6).

  • A2
  • B0
  • C12
  • D1
  • E14

Q13:

Find the radius of convergence of the power series 𝑛!𝑥2.

Q14:

Find the radius of convergence of the power series (2)𝑥𝑛+6.

  • A12
  • B0
  • C14
  • D2
  • E1

Q15:

Find the interval of convergence of the power series 3𝑛𝑥3𝑛+9.

  • A(1,1)
  • B(4,2)
  • C13,13
  • D(9,9)
  • E(3,3)

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