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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 8·(−2/3)ᵏ.

a = 8r = −2/3k₀ = 1
S =
2.Easy
kak​13579111315ε = 0.2

A ball is dropped and its first rebound reaches 3 m. Every next rebound reaches 90% of the previous one. Which rebound n is the first one lower than 0.2 m?

a₁ = 3r = 0.9ε = 0.2
n =
3.Medium
xx₀ = 2??R

Find the radius of convergence R of the power series Σk=1∞ (x − 2)ᵏ/(k·(1/2)ᵏ).

Σ (x − 2)ᵏ/(k·(1/2)ᵏ)x₀ = 2
R =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·3ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·3ᵏ/(2k)!
L =
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·22k+1/(2k + 1)!.

ak = (−1)ᵏ·22k+1/(2k + 1)!
S =
6.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 =

Answer key

  1. 1. S = −3.2
  2. 2. n = 27
  3. 3. R = 0.5
  4. 4. L = 0.75
  5. 5. S = 0.9093
  6. 6. S = 0.4055

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