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=0∞ 10·(1/4)ᵏ.

a = 10r = 1/4k₀ = 0
S =
2.Easy
kSn​12345678910S = ?

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

a = 4r = 2/5k₀ = 1
S =
3.Medium
kSn​12345678910

Find the sum S = Σk=116 2/(k(k + 1)).

ak = 2/(k(k + 1))n = 16
S =
4.Medium
AΣ (1 + 1/k)ᵏk = 1 … ∞BΣ (3/4)ᵏk = 1 … ∞CΣ 2/kk = 1 … ∞DΣ 2ᵏ/k³k = 1 … ∞

Exactly one of the four series converges. Click it.

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

f(x) = sin x is approximated at x = 0.5 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 = 0.5M = 1ε = 1 × 10⁻⁶
n =
6.Hard

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

f(x) = e−xa = 1k = 4
c₄ =

Answer key

  1. 1. S = 13.33
  2. 2. S = 2.667
  3. 3. S = 1.882
  4. 4. B: Σ (3/4)ᵏ
  5. 5. n = 7
  6. 6. c₄ = 0.01533

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