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∞ 4·(−2/5)ᵏ.

a = 4r = −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
AΣ 3ᵏ/k³k = 1 … ∞BΣ 1/(k² + 3)k = 1 … ∞CΣ 2/k³k = 1 … ∞DΣ (−1)ᵏ/√kk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 3ᵏ/k³B: Σ 1/(k² + 3)C: Σ 2/k³D: Σ (−1)ᵏ/√k
  1. 1A: Σ 3ᵏ/k³
  2. 2B: Σ 1/(k² + 3)
  3. 3C: Σ 2/k³
  4. 4D: Σ (−1)ᵏ/√k
4.Medium
AΣ (3/2)ᵏk = 1 … ∞BΣ 3ᵏ/k³k = 1 … ∞CΣ (−1)ᵏ/√kk = 1 … ∞DΣ 1/√kk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (3/2)ᵏB: Σ 3ᵏ/k³C: Σ (−1)ᵏ/√kD: Σ 1/√k
  1. 1A: Σ (3/2)ᵏ
  2. 2B: Σ 3ᵏ/k³
  3. 3C: Σ (−1)ᵏ/√k
  4. 4D: Σ 1/√k
5.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 2 at x = 1. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e1 = 2.718 to find the largest possible error |R₂|.

f(x) = eˣn = 2x = 1M = 2.718
|R₂| =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 2 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.5 = 1.649 to find the largest possible error |R₂|.

f(x) = eˣn = 2x = 0.5M = 1.649
|R₂| =

Answer key

  1. 1. S = −1.143
  2. 2. S10 = 8.926
  3. 3. A: Σ 3ᵏ/k³
  4. 4. C: Σ (−1)ᵏ/√k
  5. 5. |R₂| = 0.453
  6. 6. |R₂| = 0.03435

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