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​12345678910

Find the sum S10 of the first 10 terms of the geometric sequence 1, 2, 4, …

a₁ = 1r = 2n = 10
S10 =
2.Easy
kak​13579111315ε = 0.01

A ball is dropped and its first rebound reaches 20 m. Every next rebound reaches 70% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 20r = 0.7ε = 0.01
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 2)).

ak = 1/(k(k + 2))
S =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/3ᵏ.

Σ xᵏ/3ᵏx₀ = 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 1 × 10⁻⁵.

f(x) = eˣx = 2M = 8ε = 1 × 10⁻⁵
n =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.75ᵏ/k.

ak = (−1)k+1·0.75ᵏ/k
S =

Answer key

  1. 1. S10 = 1023
  2. 2. n = 23
  3. 3. S = 0.75
  4. 4. R = 3
  5. 5. n = 13
  6. 6. S = 0.5596

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