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=2∞ 18·(−1/2)ᵏ.

a = 18r = −1/2k₀ = 2
S =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 24·(−2/3)ᵏ.

a = 24r = −2/3k₀ = 0
S =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/(k²·5ᵏ).

Σ xᵏ/(k²·5ᵏ)x₀ = 0
R =
4.Medium
AΣ 5/k³k = 1 … ∞BΣ 1/(k(k + 2))k = 1 … ∞CΣ (−1)ᵏ/kk = 1 … ∞DΣ k!/3ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 5/k³B: Σ 1/(k(k + 2))C: Σ (−1)ᵏ/kD: Σ k!/3ᵏ
  1. 1A: Σ 5/k³
  2. 2B: Σ 1/(k(k + 2))
  3. 3C: Σ (−1)ᵏ/k
  4. 4D: Σ k!/3ᵏ
5.Hard

f(x) = sin x is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = sin xx = 2M = 1ε = 1 × 10⁻⁶
n =
6.Hard

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

ak = (−1)ᵏ/(2k + 1)!
S =

Answer key

  1. 1. S = 3
  2. 2. S = 14.4
  3. 3. R = 5
  4. 4. D: Σ k!/3ᵏ
  5. 5. n = 13
  6. 6. S = 0.8415

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