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∞ 5·(3/4)ᵏ.

a = 5r = 3/4k₀ = 0
S =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 6·(1/3)ᵏ.

a = 6r = 1/3k₀ = 1
S =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 16ᵏx²ᵏ/k.

Σ 16ᵏx²ᵏ/kx₀ = 0
R =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/(k·2ᵏ).

Σ xᵏ/(k·2ᵏ)x₀ = 0
R =
5.Hard

f(x) = eˣ 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 = 2, find the smallest degree n that guarantees an error below 0.0005.

f(x) = eˣx = 0.5M = 2ε = 0.0005
n =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·22k/(2k)!.

ak = (−1)ᵏ·22k/(2k)!
S =

Answer key

  1. 1. S = 20
  2. 2. S = 3
  3. 3. R = 0.25
  4. 4. R = 2
  5. 5. n = 5
  6. 6. S = −0.4161

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