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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 10, 20, 40, …

a₁ = 10r = 2n = 7
S7 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 1, 2, 4, …

a₁ = 1r = 2n = 9
S9 =
3.Medium
AΣ (−1)ᵏ/√kk = 1 … ∞BΣ 3ᵏ/k!k = 1 … ∞CΣ 1/(k² + 4)k = 1 … ∞DΣ k/(k + 9)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/√kB: Σ 3ᵏ/k!C: Σ 1/(k² + 4)D: Σ k/(k + 9)
  1. 1A: Σ (−1)ᵏ/√k
  2. 2B: Σ 3ᵏ/k!
  3. 3C: Σ 1/(k² + 4)
  4. 4D: Σ k/(k + 9)
4.Medium
AΣ 5/k⁴k = 1 … ∞BΣ 2ᵏ/k³k = 1 … ∞CΣ ln k / kk = 1 … ∞DΣ 1/(3k + 7)k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 5/k⁴B: Σ 2ᵏ/k³C: Σ ln k / kD: Σ 1/(3k + 7)
  1. 1A: Σ 5/k⁴
  2. 2B: Σ 2ᵏ/k³
  3. 3C: Σ ln k / k
  4. 4D: Σ 1/(3k + 7)
5.Hard

Find the coefficient c₃ of (x − 4)³ in the Taylor series of f(x) = 1/x about a = 4.

f(x) = 1/xa = 4k = 3
c₃ =
6.Hard

f(x) = sin x is approximated at x = 0.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = sin xx = 0.5M = 1ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. S7 = 1270
  2. 2. S9 = 511
  3. 3. D: Σ k/(k + 9)
  4. 4. A: Σ 5/k⁴
  5. 5. c₃ = −0.003906
  6. 6. n = 7

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