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 10, 5, 2.5, …

a₁ = 10r = 0.5n = 9
S9 =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 3, 6, 12, …

a₁ = 3r = 2n = 9
S9 =
3.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((5k + 4)/(2k + 5))ᵏ. Find L = lim |ak|1/k.

ak = ((5k + 4)/(2k + 5))ᵏ
L =
4.Medium
AΣ 2ᵏ/k!k = 1 … ∞BΣ 1/k⁴k = 1 … ∞CΣ (−1)ᵏ/√kk = 1 … ∞DΣ (3/2)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 2ᵏ/k!B: Σ 1/k⁴C: Σ (−1)ᵏ/√kD: Σ (3/2)ᵏ
  1. 1A: Σ 2ᵏ/k!
  2. 2B: Σ 1/k⁴
  3. 3C: Σ (−1)ᵏ/√k
  4. 4D: Σ (3/2)ᵏ
5.Hard

f(x) = cos x is approximated at x = 1 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) = cos xx = 1M = 1ε = 1 × 10⁻⁶
n =
6.Hard
xyfP₃0.5

Use the Maclaurin polynomial of degree 3 of f(x) = ln(1 + x) to approximate f(0.5). Give P₃(0.5).

f(x) = ln(1 + x)n = 3x = 0.5
P₃(0.5) =

Answer key

  1. 1. S9 = 19.96
  2. 2. S9 = 1533
  3. 3. L = 2.5
  4. 4. D: Σ (3/2)ᵏ
  5. 5. n = 9
  6. 6. P₃(0.5) = 0.4167

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