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=0∞ 24·(2/5)ᵏ.

a = 24r = 2/5k₀ = 0
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
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 9ᵏx²ᵏ/k.

Σ 9ᵏx²ᵏ/kx₀ = 0
R =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k·5ᵏ/2ᵏ. Find L = lim |ak+1/ak|.

ak = k·5ᵏ/2ᵏ
L =
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 1 × 10⁻⁶.

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

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.25ᵏ/k.

ak = (−1)k+1·0.25ᵏ/k
S =

Answer key

  1. 1. S = 40
  2. 2. S10 = 8.926
  3. 3. R = 0.3333
  4. 4. L = 2.5
  5. 5. n = 9
  6. 6. S = 0.2231

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