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​123456

Find the sum S6 of the first 6 terms of the geometric sequence 0.5, −0.25, 0.125, …

a₁ = 0.5r = −0.5n = 6
S6 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 6·(−1/3)ᵏ.

a = 6r = −1/3k₀ = 0
S =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ k!·xᵏ/kᵏ.

Σ k!·xᵏ/kᵏx₀ = 0
R =
4.Medium
AΣ (2k + 1)/(k + 2)k = 1 … ∞BΣ (5/4)ᵏk = 1 … ∞CΣ 3ᵏ/k³k = 1 … ∞DΣ 1/k²k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (2k + 1)/(k + 2)B: Σ (5/4)ᵏC: Σ 3ᵏ/k³D: Σ 1/k²
  1. 1A: Σ (2k + 1)/(k + 2)
  2. 2B: Σ (5/4)ᵏ
  3. 3C: Σ 3ᵏ/k³
  4. 4D: Σ 1/k²
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.25ᵏ.

ak = k·0.25ᵏ
S =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 2 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₂|.

f(x) = sin xn = 2x = 0.3M = 1
|R₂| =

Answer key

  1. 1. S6 = 0.3281
  2. 2. S = 4.5
  3. 3. R = 2.718
  4. 4. D: Σ 1/k²
  5. 5. S = 0.4444
  6. 6. |R₂| = 0.0045

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