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∞ 9·(−2/5)ᵏ.

a = 9r = −2/5k₀ = 1
S =
2.Easy
kak​123456789101112

The arithmetic sequence 4, 6, 8, 10, … ends with the term 50. How many terms n does it have?

a₁ = 4d = 2aₙ = 50
n =
3.Medium
AΣ 1/(4k + 3)k = 1 … ∞BΣ (1 + 1/k)ᵏk = 1 … ∞CΣ ln k / kk = 1 … ∞DΣ 1/(3ᵏ + k)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 1/(4k + 3)B: Σ (1 + 1/k)ᵏC: Σ ln k / kD: Σ 1/(3ᵏ + k)
  1. 1A: Σ 1/(4k + 3)
  2. 2B: Σ (1 + 1/k)ᵏ
  3. 3C: Σ ln k / k
  4. 4D: Σ 1/(3ᵏ + k)
4.Medium
AΣ k³/3ᵏk = 1 … ∞BΣ 5/k³k = 1 … ∞CΣ k!/3ᵏk = 1 … ∞DΣ (−1)ᵏ/√kk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k³/3ᵏB: Σ 5/k³C: Σ k!/3ᵏD: Σ (−1)ᵏ/√k
  1. 1A: Σ k³/3ᵏ
  2. 2B: Σ 5/k³
  3. 3C: Σ k!/3ᵏ
  4. 4D: Σ (−1)ᵏ/√k
5.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·1.52k+1/(2k + 1)!.

ak = (−1)ᵏ·1.52k+1/(2k + 1)!
S =
6.Hard

f(x) = eˣ is approximated at x = 1 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 3, find the smallest degree n that guarantees an error below 1 × 10⁻⁵.

f(x) = eˣx = 1M = 3ε = 1 × 10⁻⁵
n =

Answer key

  1. 1. S = −2.571
  2. 2. n = 24
  3. 3. D: Σ 1/(3ᵏ + k)
  4. 4. C: Σ k!/3ᵏ
  5. 5. S = 0.9975
  6. 6. n = 8

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