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∞ 2·(−3/4)ᵏ.

a = 2r = −3/4k₀ = 2
S =
2.Easy
kak​13579111315ε = 0.2

The geometric sequence aₙ = 5·0.85ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.2.

a₁ = 5r = 0.85ε = 0.2
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 1)).

ak = 1/(k(k + 1))
S =
4.Medium
AΣ k/(k + 9)k = 1 … ∞BΣ k!/10ᵏk = 1 … ∞CΣ (5/4)ᵏk = 1 … ∞DΣ (−1)ᵏ/kk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ k/(k + 9)B: Σ k!/10ᵏC: Σ (5/4)ᵏD: Σ (−1)ᵏ/k
  1. 1A: Σ k/(k + 9)
  2. 2B: Σ k!/10ᵏ
  3. 3C: Σ (5/4)ᵏ
  4. 4D: Σ (−1)ᵏ/k
5.Hard

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = 1/x about a = 1.

f(x) = 1/xa = 1k = 4
c₄ =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 3 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e1.5 = 4.482 to find the largest possible error |R₃|.

f(x) = eˣn = 3x = 1.5M = 4.482
|R₃| =

Answer key

  1. 1. S = 0.6429
  2. 2. n = 21
  3. 3. S = 1
  4. 4. D: Σ (−1)ᵏ/k
  5. 5. c₄ = 1
  6. 6. |R₃| = 0.9454

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