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​12345678

Find the sum S8 of the first 8 terms of the geometric sequence 10, 15, 22.5, …

a₁ = 10r = 1.5n = 8
S8 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 10·(−1/2)ᵏ.

a = 10r = −1/2k₀ = 2
S =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ 2ᵏ·k!/kᵏ. Find L = lim |ak+1/ak|.

ak = 2ᵏ·k!/kᵏ
L =
4.Medium
AΣ (−1)ᵏ/√kk = 1 … ∞BΣ 1/(k² + 6)k = 1 … ∞CΣ (4/3)ᵏk = 1 … ∞DΣ (3/5)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/√kB: Σ 1/(k² + 6)C: Σ (4/3)ᵏD: Σ (3/5)ᵏ
  1. 1A: Σ (−1)ᵏ/√k
  2. 2B: Σ 1/(k² + 6)
  3. 3C: Σ (4/3)ᵏ
  4. 4D: Σ (3/5)ᵏ
5.Hard

f(x) = sin 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 0.001.

f(x) = sin xx = 1M = 1ε = 0.001
n =
6.Hard

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

Answer key

  1. 1. S8 = 492.6
  2. 2. S = 1.667
  3. 3. L = 0.7358
  4. 4. C: Σ (4/3)ᵏ
  5. 5. n = 6
  6. 6. n = 9

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