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​12345

Find the sum S5 of the first 5 terms of the geometric sequence 1, 0.5, 0.25, …

a₁ = 1r = 0.5n = 5
S5 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 12·(−2/5)ᵏ.

a = 12r = −2/5k₀ = 2
S =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/3ᵏ.

Σ xᵏ/3ᵏx₀ = 0
R =
4.Medium
AΣ k/2ᵏk = 1 … ∞BΣ (−1)ᵏ/√kk = 1 … ∞CΣ 2ᵏ/k³k = 1 … ∞DΣ 1/(2ᵏ + k)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k/2ᵏB: Σ (−1)ᵏ/√kC: Σ 2ᵏ/k³D: Σ 1/(2ᵏ + k)
  1. 1A: Σ k/2ᵏ
  2. 2B: Σ (−1)ᵏ/√k
  3. 3C: Σ 2ᵏ/k³
  4. 4D: Σ 1/(2ᵏ + k)
5.Hard

f(x) = eˣ 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 = 2, find the smallest degree n that guarantees an error below 0.001.

f(x) = eˣx = 0.5M = 2ε = 0.001
n =
6.Hard

f(x) = eˣ is approximated at x = 1 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 3, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = eˣx = 1M = 3ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. S5 = 1.938
  2. 2. S = 1.371
  3. 3. R = 3
  4. 4. C: Σ 2ᵏ/k³
  5. 5. n = 4
  6. 6. n = 9

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