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​12345678ε = 0.2

The geometric sequence aₙ = 3·0.6ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.2.

a₁ = 3r = 0.6ε = 0.2
n =
2.Easy
kak​1234567891011ε = 0.01

A ball is dropped and its first rebound reaches 3 m. Every next rebound reaches 50% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 3r = 0.5ε = 0.01
n =
3.Medium
AΣ k/(k + 7)k = 1 … ∞BΣ (−1)ᵏ/√kk = 1 … ∞CΣ ln k / kk = 1 … ∞DΣ (4/3)ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ k/(k + 7)B: Σ (−1)ᵏ/√kC: Σ ln k / kD: Σ (4/3)ᵏ
  1. 1A: Σ k/(k + 7)
  2. 2B: Σ (−1)ᵏ/√k
  3. 3C: Σ ln k / k
  4. 4D: Σ (4/3)ᵏ
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 16ᵏx²ᵏ/k.

Σ 16ᵏx²ᵏ/kx₀ = 0
R =
5.Hard

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

f(x) = e−xa = −1k = 2
c₂ =
6.Hard

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

ak = (−1)ᵏ/(2k + 1)!
S =

Answer key

  1. 1. n = 7
  2. 2. n = 10
  3. 3. B: Σ (−1)ᵏ/√k
  4. 4. R = 0.25
  5. 5. c₂ = 1.359
  6. 6. S = 0.8415

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