Sequences & series worksheet with answers

Free printable Sequences & series worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 9·(2/3)ᵏ.

a = 9r = 2/3k₀ = 0
S =
2.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 10, 20, 40, …

a₁ = 10r = 2n = 7
S7 =
3.Medium
xx₀ = −1??R

Find the radius of convergence R of the power series Σk=1∞ (x + 1)ᵏ/2ᵏ.

Σ (x + 1)ᵏ/2ᵏx₀ = −1
R =
4.Medium
AΣ (−1)ᵏ/√kk = 1 … ∞BΣ 5/k⁴k = 1 … ∞CΣ 1/√kk = 1 … ∞DΣ 1/(k² + 8)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/√kB: Σ 5/k⁴C: Σ 1/√kD: Σ 1/(k² + 8)
  1. 1A: Σ (−1)ᵏ/√k
  2. 2B: Σ 5/k⁴
  3. 3C: Σ 1/√k
  4. 4D: Σ 1/(k² + 8)
5.Hard
xyfP₄0.5

Use the Maclaurin polynomial of degree 4 of f(x) = 1/(1 + x) to approximate f(0.5). Give P₄(0.5).

f(x) = 1/(1 + x)n = 4x = 0.5
P₄(0.5) =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ 0.5ᵏ/k!.

ak = 0.5ᵏ/k!
S =

Answer key

  1. 1. S = 27
  2. 2. S7 = 1270
  3. 3. R = 2
  4. 4. C: Σ 1/√k
  5. 5. P₄(0.5) = 0.6875
  6. 6. S = 1.649

Full step-by-step solutions: practise this topic on examproblems.com.