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=2∞ 8·(−1/3)ᵏ.

a = 8r = −1/3k₀ = 2
S =
2.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 2, −1, 0.5, …

a₁ = 2r = −0.5n = 7
S7 =
3.Medium
AΣ 1/(3ᵏ + k)k = 1 … ∞BΣ (1/3)ᵏk = 1 … ∞CΣ (−1)ᵏ/kk = 1 … ∞DΣ k!/3ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/(3ᵏ + k)B: Σ (1/3)ᵏC: Σ (−1)ᵏ/kD: Σ k!/3ᵏ
  1. 1A: Σ 1/(3ᵏ + k)
  2. 2B: Σ (1/3)ᵏ
  3. 3C: Σ (−1)ᵏ/k
  4. 4D: Σ k!/3ᵏ
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 2)).

ak = 12/(k(k + 2))
S =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·1.52k+1/(2k + 1)!.

ak = (−1)ᵏ·1.52k+1/(2k + 1)!
S =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 5 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = sin xn = 5x = 0.5M = 1
|R₅| =

Answer key

  1. 1. S = 0.6667
  2. 2. S7 = 1.344
  3. 3. D: Σ k!/3ᵏ
  4. 4. S = 9
  5. 5. S = 0.9975
  6. 6. |R₅| = 2.17 × 10⁻⁵

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