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 5, 15, 45, …

a₁ = 5r = 3n = 8
S8 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 4·(−3/4)ᵏ.

a = 4r = −3/4k₀ = 1
S =
3.Medium
xx₀ = 0??R

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

Σ k!·xᵏ/kᵏx₀ = 0
R =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/(k·4ᵏ).

Σ xᵏ/(k·4ᵏ)x₀ = 0
R =
5.Hard
xyfP₄0.25

Use the Maclaurin polynomial of degree 4 of f(x) = 1/(1 − 2x) to approximate f(0.25). Give P₄(0.25).

f(x) = 1/(1 − 2x)n = 4x = 0.25
P₄(0.25) =
6.Hard

f(x) = cos x 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 = 1, find the smallest degree n that guarantees an error below 1 × 10⁻⁵.

f(x) = cos xx = 0.5M = 1ε = 1 × 10⁻⁵
n =

Answer key

  1. 1. S8 = 16400
  2. 2. S = −1.714
  3. 3. R = 2.718
  4. 4. R = 4
  5. 5. P₄(0.25) = 1.938
  6. 6. n = 6

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