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​12345

Find the sum S5 of the first 5 terms of the geometric sequence 0.5, 0.6, 0.72, …

a₁ = 0.5r = 1.2n = 5
S5 =
2.Easy
kak​1234567ε = 0.1

The geometric sequence aₙ = 2·0.5ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 2r = 0.5ε = 0.1
n =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ 3ᵏ·k!/kᵏ. Find L = lim |ak+1/ak|.

ak = 3ᵏ·k!/kᵏ
L =
4.Medium
AΣ (−1)ᵏ/√kk = 1 … ∞BΣ ln k / kk = 1 … ∞CΣ 1/(k(k + 1))k = 1 … ∞DΣ (3/5)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/√kB: Σ ln k / kC: Σ 1/(k(k + 1))D: Σ (3/5)ᵏ
  1. 1A: Σ (−1)ᵏ/√k
  2. 2B: Σ ln k / k
  3. 3C: Σ 1/(k(k + 1))
  4. 4D: Σ (3/5)ᵏ
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.25ᵏ.

ak = k·0.25ᵏ
S =
6.Hard

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = ∛x about a = 1.

f(x) = ∛xa = 1k = 4
c₄ =

Answer key

  1. 1. S5 = 3.721
  2. 2. n = 6
  3. 3. L = 1.104
  4. 4. B: Σ ln k / k
  5. 5. S = 0.4444
  6. 6. c₄ = −0.04115

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