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​13579111315ε = 0.5

A ball is dropped and its first rebound reaches 20 m. Every next rebound reaches 80% of the previous one. Which rebound n is the first one lower than 0.5 m?

a₁ = 20r = 0.8ε = 0.5
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 9·(−2/5)ᵏ.

a = 9r = −2/5k₀ = 1
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 5/(k(k + 3)).

ak = 5/(k(k + 3))
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 3)).

ak = 12/(k(k + 3))
S =
5.Hard

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

ak = (−1)ᵏ·22k+1/(2k + 1)!
S =
6.Hard

f(x) = sin x is approximated at x = 2 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 0.001.

f(x) = sin xx = 2M = 1ε = 0.001
n =

Answer key

  1. 1. n = 18
  2. 2. S = −2.571
  3. 3. S = 3.056
  4. 4. S = 7.333
  5. 5. S = 0.9093
  6. 6. n = 9

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