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.

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1.Easy
kak​13579111315ε = 0.01

The geometric sequence aₙ = 2·0.85ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.01.

a₁ = 2r = 0.85ε = 0.01
n =
2.Easy
kak​123456789101112

Find the sum S20 of the first 20 terms of the arithmetic sequence −8, −2, 4, 10, …

a₁ = −8d = 6n = 20
S20 =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ k!·xᵏ/kᵏ.

Σ k!·xᵏ/kᵏx₀ = 0
R =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 4)).

ak = 5/(k(k + 4))
S =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·22k/(2k)!.

ak = (−1)ᵏ·22k/(2k)!
S =
6.Hard

f(x) = cos x is approximated at x = 1.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 0.0005.

f(x) = cos xx = 1.5M = 1ε = 0.0005
n =

Answer key

  1. 1. n = 34
  2. 2. S20 = 980
  3. 3. R = 2.718
  4. 4. S = 2.604
  5. 5. S = −0.4161
  6. 6. n = 8

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