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​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 0.5, −1.5, 4.5, …

a₁ = 0.5r = −3n = 9
S9 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 10·(2/5)ᵏ.

a = 10r = 2/5k₀ = 0
S =
3.Medium
xx₀ = −2??R

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

Σ (2k)!·(x + 2)ᵏ/(k!)²x₀ = −2
R =
4.Medium
AΣ (3/5)ᵏk = 1 … ∞BΣ (7/4)ᵏk = 1 … ∞CΣ (k + 3)/k²k = 1 … ∞DΣ 1/(4k + 2)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (3/5)ᵏB: Σ (7/4)ᵏC: Σ (k + 3)/k²D: Σ 1/(4k + 2)
  1. 1A: Σ (3/5)ᵏ
  2. 2B: Σ (7/4)ᵏ
  3. 3C: Σ (k + 3)/k²
  4. 4D: Σ 1/(4k + 2)
5.Hard

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

f(x) = e−xa = 2k = 2
c₂ =
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. S9 = 2461
  2. 2. S = 16.67
  3. 3. R = 0.25
  4. 4. A: Σ (3/5)ᵏ
  5. 5. c₂ = 0.06767
  6. 6. c₃ = 0.04167

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