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∞ 5·(1/2)ᵏ.

a = 5r = 1/2k₀ = 1
S =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 3, 6, 12, …

a₁ = 3r = 2n = 5
S5 =
3.Medium
AΣ 1/(k(k + 2))k = 1 … ∞BΣ (5/3)ᵏk = 1 … ∞CΣ 1/√kk = 1 … ∞DΣ ln k / kk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 1/(k(k + 2))B: Σ (5/3)ᵏC: Σ 1/√kD: Σ ln k / k
  1. 1A: Σ 1/(k(k + 2))
  2. 2B: Σ (5/3)ᵏ
  3. 3C: Σ 1/√k
  4. 4D: Σ ln k / k
4.Medium
kSn​12345678910

Find the sum S = Σk=140 6/(k(k + 1)).

ak = 6/(k(k + 1))n = 40
S =
5.Hard

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

ak = k·(1/3)ᵏ
S =
6.Hard

Find the coefficient c₃ of (x + 1)³ in the Taylor series of f(x) = e2x about a = −1.

f(x) = e2xa = −1k = 3
c₃ =

Answer key

  1. 1. S = 5
  2. 2. S5 = 93
  3. 3. A: Σ 1/(k(k + 2))
  4. 4. S = 5.854
  5. 5. S = 0.75
  6. 6. c₃ = 0.1804

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