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 = 0.5

The geometric sequence aₙ = 2·0.9ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.5.

a₁ = 2r = 0.9ε = 0.5
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 18·(1/2)ᵏ.

a = 18r = 1/2k₀ = 1
S =
3.Medium
AΣ 1/k³k = 1 … ∞BΣ (−1)ᵏ/√kk = 1 … ∞CΣ (5k + 1)/(k + 2)k = 1 … ∞DΣ (1/2)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/k³B: Σ (−1)ᵏ/√kC: Σ (5k + 1)/(k + 2)D: Σ (1/2)ᵏ
  1. 1A: Σ 1/k³
  2. 2B: Σ (−1)ᵏ/√k
  3. 3C: Σ (5k + 1)/(k + 2)
  4. 4D: Σ (1/2)ᵏ
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 5ᵏ·xᵏ/(k + 1).

Σ 5ᵏ·xᵏ/(k + 1)x₀ = 0
R =
5.Hard

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

f(x) = √xa = 4k = 2
c₂ =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ 1.5ᵏ/k!.

ak = 1.5ᵏ/k!
S =

Answer key

  1. 1. n = 15
  2. 2. S = 18
  3. 3. C: Σ (5k + 1)/(k + 2)
  4. 4. R = 0.2
  5. 5. c₂ = −0.01563
  6. 6. S = 4.482

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