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​12345678ε = 0.05

A ball is dropped and its first rebound reaches 3 m. Every next rebound reaches 50% of the previous one. Which rebound n is the first one lower than 0.05 m?

a₁ = 3r = 0.5ε = 0.05
n =
2.Easy
kak​12345678910

Find the sum S10 of the first 10 terms of the geometric sequence 1, 1.2, 1.44, …

a₁ = 1r = 1.2n = 10
S10 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k²·3ᵏ/4ᵏ. Find L = lim |ak+1/ak|.

ak = k²·3ᵏ/4ᵏ
L =
4.Medium
xx₀ = 0??R

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

Σ xᵏ/2ᵏx₀ = 0
R =
5.Hard

f(x) = eˣ is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 8, find the smallest degree n that guarantees an error below 0.0005.

f(x) = eˣx = 2M = 8ε = 0.0005
n =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·0.82k/(2k)!.

ak = (−1)ᵏ·0.82k/(2k)!
S =

Answer key

  1. 1. n = 7
  2. 2. S10 = 25.96
  3. 3. L = 0.75
  4. 4. R = 2
  5. 5. n = 10
  6. 6. S = 0.6967

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