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 = 0.01

A ball is dropped and its first rebound reaches 8 m. Every next rebound reaches 70% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 8r = 0.7ε = 0.01
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 2·(−1/3)ᵏ.

a = 2r = −1/3k₀ = 0
S =
3.Medium
AΣ 2/kk = 1 … ∞BΣ (1/3)ᵏk = 1 … ∞CΣ k!/10ᵏk = 1 … ∞DΣ (4/3)ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 2/kB: Σ (1/3)ᵏC: Σ k!/10ᵏD: Σ (4/3)ᵏ
  1. 1A: Σ 2/k
  2. 2B: Σ (1/3)ᵏ
  3. 3C: Σ k!/10ᵏ
  4. 4D: Σ (4/3)ᵏ
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 9ᵏx²ᵏ/k.

Σ 9ᵏx²ᵏ/kx₀ = 0
R =
5.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 =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ k·(1/3)ᵏ.

ak = k·(1/3)ᵏ
S =

Answer key

  1. 1. n = 20
  2. 2. S = 1.5
  3. 3. B: Σ (1/3)ᵏ
  4. 4. R = 0.3333
  5. 5. S = 0.4055
  6. 6. S = 0.75

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