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 = 8·0.6ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.01.

a₁ = 8r = 0.6ε = 0.01
n =
2.Easy
kak​123456ε = 0.5

The geometric sequence aₙ = 3·0.6ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.5.

a₁ = 3r = 0.6ε = 0.5
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 2)).

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

Exactly one of the four series diverges. Click it.

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

Recognise the series and find its sum: S = Σk=1∞ k·0.2ᵏ.

ak = k·0.2ᵏ
S =
6.Hard
xyfP₄1.5

Use the Maclaurin polynomial of degree 4 of f(x) = e−x to approximate f(1.5). Give P₄(1.5).

f(x) = e−xn = 4x = 1.5
P₄(1.5) =

Answer key

  1. 1. n = 15
  2. 2. n = 5
  3. 3. S = 0.75
  4. 4. C: Σ 1/(4k + 1)
  5. 5. S = 0.3125
  6. 6. P₄(1.5) = 0.2734

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