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​123456789101112

Find the sum S18 of the first 18 terms of the arithmetic sequence −10, −8, −6, −4, …

a₁ = −10d = 2n = 18
S18 =
2.Easy
kak​123456789101112

Find the sum S15 of the first 15 terms of the arithmetic sequence 18, 15, 12, 9, …

a₁ = 18d = −3n = 15
S15 =
3.Medium
xx₀ = 1??R

The power series Σk=1∞ (2k)!·(x − 1)ᵏ/(k!)² converges on an interval around x₀ = 1. Find the right end x of that interval.

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

Exactly one of the four series diverges. Click it.

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

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

f(x) = ∛xa = 1k = 3
c₃ =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 3 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.3 = 1.35 to find the largest possible error |R₃|.

f(x) = eˣn = 3x = 0.3M = 1.35
|R₃| =

Answer key

  1. 1. S18 = 126
  2. 2. S15 = −45
  3. 3. x = 1.25
  4. 4. C: Σ (5/3)ᵏ
  5. 5. c₃ = 0.06173
  6. 6. |R₃| = 0.0004556

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