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·(1/2)ᵏ.

a = 8r = 1/2k₀ = 1
S =
2.Easy
kak​123456789101112

Find the sum S31 of the first 31 terms of the arithmetic sequence 14, 14.5, 15, 15.5, …

a₁ = 14d = 0.5n = 31
S31 =
3.Medium
AΣ (5/4)ᵏk = 1 … ∞BΣ (1 + 1/k)ᵏk = 1 … ∞CΣ 3ᵏ/k³k = 1 … ∞DΣ (4/5)ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (5/4)ᵏB: Σ (1 + 1/k)ᵏC: Σ 3ᵏ/k³D: Σ (4/5)ᵏ
  1. 1A: Σ (5/4)ᵏ
  2. 2B: Σ (1 + 1/k)ᵏ
  3. 3C: Σ 3ᵏ/k³
  4. 4D: Σ (4/5)ᵏ
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 3)).

ak = 1/(k(k + 3))
S =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 4 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = sin xn = 4x = 0.2M = 1
|R₄| =
6.Hard

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = 1/x about a = 1.

f(x) = 1/xa = 1k = 4
c₄ =

Answer key

  1. 1. S = 8
  2. 2. S31 = 666.5
  3. 3. D: Σ (4/5)ᵏ
  4. 4. S = 0.6111
  5. 5. |R₄| = 2.667 × 10⁻⁶
  6. 6. c₄ = 1

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