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∞ 9·(−1/3)ᵏ.

a = 9r = −1/3k₀ = 1
S =
2.Easy
kak​12345678910

Find the sum S10 of the first 10 terms of the geometric sequence 2, 1, 0.5, …

a₁ = 2r = 0.5n = 10
S10 =
3.Medium
AΣ 1/(k(k + 3))k = 1 … ∞BΣ 2ᵏ/k!k = 1 … ∞CΣ (1/3)ᵏk = 1 … ∞DΣ 5/kk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/(k(k + 3))B: Σ 2ᵏ/k!C: Σ (1/3)ᵏD: Σ 5/k
  1. 1A: Σ 1/(k(k + 3))
  2. 2B: Σ 2ᵏ/k!
  3. 3C: Σ (1/3)ᵏ
  4. 4D: Σ 5/k
4.Medium
kSn​12345678910

Find the sum S = Σk=133 1/(k(k + 1)).

ak = 1/(k(k + 1))n = 33
S =
5.Hard
xyfP₄−0.5

Use the Maclaurin polynomial of degree 4 of f(x) = cos(3x) to approximate f(−0.5). Give P₄(−0.5).

f(x) = cos(3x)n = 4x = −0.5
P₄(−0.5) =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 3 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e1.5 = 4.482 to find the largest possible error |R₃|.

f(x) = eˣn = 3x = 1.5M = 4.482
|R₃| =

Answer key

  1. 1. S = −2.25
  2. 2. S10 = 3.996
  3. 3. D: Σ 5/k
  4. 4. S = 0.9706
  5. 5. P₄(−0.5) = 0.08594
  6. 6. |R₃| = 0.9454

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