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=1∞ 8·(4/5)ᵏ.

a = 8r = 4/5k₀ = 1
S =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 18·(−2/5)ᵏ.

a = 18r = −2/5k₀ = 1
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 2)).

ak = 5/(k(k + 2))
S =
4.Medium
AΣ ln k / kk = 1 … ∞BΣ (3/2)ᵏk = 1 … ∞CΣ 1/(k² + 1)k = 1 … ∞DΣ (2k + 1)/(k + 2)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ ln k / kB: Σ (3/2)ᵏC: Σ 1/(k² + 1)D: Σ (2k + 1)/(k + 2)
  1. 1A: Σ ln k / k
  2. 2B: Σ (3/2)ᵏ
  3. 3C: Σ 1/(k² + 1)
  4. 4D: Σ (2k + 1)/(k + 2)
5.Hard

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

ak = 0.5ᵏ/k!
S =
6.Hard

f(x) = eˣ is approximated at x = 1 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 3, find the smallest degree n that guarantees an error below 0.001.

f(x) = eˣx = 1M = 3ε = 0.001
n =

Answer key

  1. 1. S = 32
  2. 2. S = −5.143
  3. 3. S = 3.75
  4. 4. C: Σ 1/(k² + 1)
  5. 5. S = 1.649
  6. 6. n = 6

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