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​13579111315ε = 0.01

The geometric sequence aₙ = 8·0.85ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.01.

a₁ = 8r = 0.85ε = 0.01
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 8·(−2/5)ᵏ.

a = 8r = −2/5k₀ = 0
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 1)).

ak = 1/(k(k + 1))
S =
4.Medium
AΣ (5k + 1)/(k + 2)k = 1 … ∞BΣ (1/3)ᵏk = 1 … ∞CΣ 1/(k(k + 2))k = 1 … ∞DΣ 1/k³k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (5k + 1)/(k + 2)B: Σ (1/3)ᵏC: Σ 1/(k(k + 2))D: Σ 1/k³
  1. 1A: Σ (5k + 1)/(k + 2)
  2. 2B: Σ (1/3)ᵏ
  3. 3C: Σ 1/(k(k + 2))
  4. 4D: Σ 1/k³
5.Hard
xyfP₂−1

Use the Maclaurin polynomial of degree 2 of f(x) = cos x to approximate f(−1). Give P₂(−1).

f(x) = cos xn = 2x = −1
P₂(−1) =
6.Hard

Find the coefficient c₃ of (x − 2)³ in the Taylor series of f(x) = ln x about a = 2.

f(x) = ln xa = 2k = 3
c₃ =

Answer key

  1. 1. n = 43
  2. 2. S = 5.714
  3. 3. S = 1
  4. 4. A: Σ (5k + 1)/(k + 2)
  5. 5. P₂(−1) = 0.5
  6. 6. c₃ = 0.04167

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