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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Name: ____________________   Date: ____________

1.Easy
kak​123456789101112

Find the sum S16 of the first 16 terms of the arithmetic sequence −10, −6, −2, 2, …

a₁ = −10d = 4n = 16
S16 =
2.Easy
kSn​12345678910S = ?

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

a = 2r = 1/4k₀ = 1
S =
3.Medium
AΣ (5/3)ᵏk = 1 … ∞BΣ 3ᵏ/k³k = 1 … ∞CΣ ln k / kk = 1 … ∞DΣ 1/(2ᵏ + k)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (5/3)ᵏB: Σ 3ᵏ/k³C: Σ ln k / kD: Σ 1/(2ᵏ + k)
  1. 1A: Σ (5/3)ᵏ
  2. 2B: Σ 3ᵏ/k³
  3. 3C: Σ ln k / k
  4. 4D: Σ 1/(2ᵏ + k)
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 1)).

ak = 2/(k(k + 1))
S =
5.Hard
xyfP₃0.5

Use the Maclaurin polynomial of degree 3 of f(x) = ln(1 − x) to approximate f(0.5). Give P₃(0.5).

f(x) = ln(1 − x)n = 3x = 0.5
P₃(0.5) =
6.Hard

Find the coefficient c₃ of (x − 5)³ in the Taylor series of f(x) = 1/x about a = 5.

f(x) = 1/xa = 5k = 3
c₃ =

Answer key

  1. 1. S16 = 320
  2. 2. S = 0.6667
  3. 3. D: Σ 1/(2ᵏ + k)
  4. 4. S = 2
  5. 5. P₃(0.5) = −0.6667
  6. 6. c₃ = −0.0016

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