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 = 0.2

The geometric sequence aₙ = 8·0.75ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.2.

a₁ = 8r = 0.75ε = 0.2
n =
2.Easy
kak​13579111315ε = 0.01

A ball is dropped and its first rebound reaches 10 m. Every next rebound reaches 85% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 10r = 0.85ε = 0.01
n =
3.Medium
kSn​12345678910

Find the sum S = Σk=137 2/(k(k + 1)).

ak = 2/(k(k + 1))n = 37
S =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 25ᵏx²ᵏ/k.

Σ 25ᵏx²ᵏ/kx₀ = 0
R =
5.Hard

Find the coefficient c₂ of (x − 4)² in the Taylor series of f(x) = 1/x about a = 4.

f(x) = 1/xa = 4k = 2
c₂ =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.5ᵏ/k.

ak = (−1)k+1·0.5ᵏ/k
S =

Answer key

  1. 1. n = 14
  2. 2. n = 44
  3. 3. S = 1.947
  4. 4. R = 0.2
  5. 5. c₂ = 0.01563
  6. 6. S = 0.4055

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