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​123456789101112ε = 0.1

A ball is dropped and its first rebound reaches 3 m. Every next rebound reaches 70% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 3r = 0.7ε = 0.1
n =
2.Easy
kak​13579111315ε = 0.01

A ball is dropped and its first rebound reaches 2 m. Every next rebound reaches 85% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 2r = 0.85ε = 0.01
n =
3.Medium
AΣ ln k / kk = 1 … ∞BΣ (5/4)ᵏk = 1 … ∞CΣ 1/(k² + 2)k = 1 … ∞DΣ (2k + 1)/(k + 2)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ ln k / kB: Σ (5/4)ᵏC: Σ 1/(k² + 2)D: Σ (2k + 1)/(k + 2)
  1. 1A: Σ ln k / k
  2. 2B: Σ (5/4)ᵏ
  3. 3C: Σ 1/(k² + 2)
  4. 4D: Σ (2k + 1)/(k + 2)
4.Medium
AΣ (−1)ᵏ/√kk = 1 … ∞BΣ 1/√kk = 1 … ∞CΣ 1/k⁴k = 1 … ∞DΣ (2/5)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/√kB: Σ 1/√kC: Σ 1/k⁴D: Σ (2/5)ᵏ
  1. 1A: Σ (−1)ᵏ/√k
  2. 2B: Σ 1/√k
  3. 3C: Σ 1/k⁴
  4. 4D: Σ (2/5)ᵏ
5.Hard
xyfP₂0.5

Use the Maclaurin polynomial of degree 2 of f(x) = e2x to approximate f(0.5). Give P₂(0.5).

f(x) = e2xn = 2x = 0.5
P₂(0.5) =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.75ᵏ/k.

ak = (−1)k+1·0.75ᵏ/k
S =

Answer key

  1. 1. n = 11
  2. 2. n = 34
  3. 3. C: Σ 1/(k² + 2)
  4. 4. B: Σ 1/√k
  5. 5. P₂(0.5) = 2.5
  6. 6. S = 0.5596

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