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=1∞ 5·(−2/5)ᵏ.

a = 5r = −2/5k₀ = 1
S =
2.Easy
kak​12345678910

Find the sum S10 of the first 10 terms of the geometric sequence 2, 1.6, 1.28, …

a₁ = 2r = 0.8n = 10
S10 =
3.Medium
xx₀ = 1??R

Find the radius of convergence R of the power series Σk=1∞ 2ᵏ·(x − 1)ᵏ/(k + 1).

Σ 2ᵏ·(x − 1)ᵏ/(k + 1)x₀ = 1
R =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 2)).

ak = 5/(k(k + 2))
S =
5.Hard

Find the coefficient c₂ of (x − 4)² in the Taylor series of f(x) = 1/x about a = 4.

f(x) = 1/xa = 4k = 2
c₂ =
6.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) =

Answer key

  1. 1. S = −1.429
  2. 2. S10 = 8.926
  3. 3. R = 0.5
  4. 4. S = 3.75
  5. 5. c₂ = 0.01563
  6. 6. P₃(0.5) = −0.6667

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