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 1, −0.5, 0.25, …

a₁ = 1r = −0.5n = 9
S9 =
2.Easy
kak​12345

Find the sum S5 of the first 5 terms of the geometric sequence 2, −4, 8, …

a₁ = 2r = −2n = 5
S5 =
3.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 =
4.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 =
5.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 5 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 5! = 120 to find the largest possible error |R₅|.

f(x) = ln(1 + x)n = 5x = 0.5M = 120
|R₅| =
6.Hard
xyfP₃0.4

Use the Maclaurin polynomial of degree 3 of f(x) = 1/(1 − x) to approximate f(0.4). Give P₃(0.4).

f(x) = 1/(1 − x)n = 3x = 0.4
P₃(0.4) =

Answer key

  1. 1. S9 = 0.668
  2. 2. S5 = 22
  3. 3. R = 4
  4. 4. R = 2.718
  5. 5. |R₅| = 0.002604
  6. 6. P₃(0.4) = 1.624

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