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​1234567891011ε = 0.1

The geometric sequence aₙ = 8·0.6ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 8r = 0.6ε = 0.1
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 5·(1/4)ᵏ.

a = 5r = 1/4k₀ = 2
S =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 4ᵏx²ᵏ/k.

Σ 4ᵏx²ᵏ/kx₀ = 0
R =
4.Medium
AΣ (1/3)ᵏk = 1 … ∞BΣ (1 + 1/k)ᵏk = 1 … ∞CΣ (7/4)ᵏk = 1 … ∞DΣ 1/kk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (1/3)ᵏB: Σ (1 + 1/k)ᵏC: Σ (7/4)ᵏD: Σ 1/k
  1. 1A: Σ (1/3)ᵏ
  2. 2B: Σ (1 + 1/k)ᵏ
  3. 3C: Σ (7/4)ᵏ
  4. 4D: Σ 1/k
5.Hard

Recognise the series and find its sum: S = Σk=0∞ 0.5ᵏ/k!.

ak = 0.5ᵏ/k!
S =
6.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 3 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 3! = 6 to find the largest possible error |R₃|.

f(x) = ln(1 + x)n = 3x = 0.3M = 6
|R₃| =

Answer key

  1. 1. n = 10
  2. 2. S = 0.4167
  3. 3. R = 0.5
  4. 4. A: Σ (1/3)ᵏ
  5. 5. S = 1.649
  6. 6. |R₃| = 0.002025

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