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 = 0.1

A ball is dropped and its first rebound reaches 8 m. Every next rebound reaches 70% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 8r = 0.7ε = 0.1
n =
2.Easy
kak​123456

Find the sum S6 of the first 6 terms of the geometric sequence 5, 2.5, 1.25, …

a₁ = 5r = 0.5n = 6
S6 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ kᵏ/(2ᵏ·k!). Find L = lim |ak+1/ak|.

ak = kᵏ/(2ᵏ·k!)
L =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 6/(k(k + 4)).

ak = 6/(k(k + 4))
S =
5.Hard

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

ak = (−1)ᵏ·22k/(2k)!
S =
6.Hard

f(x) = cos x is approximated at x = 1 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 1 × 10⁻⁶.

f(x) = cos xx = 1M = 1ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. n = 14
  2. 2. S6 = 9.844
  3. 3. L = 1.359
  4. 4. S = 3.125
  5. 5. S = −0.4161
  6. 6. n = 9

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