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 arithmetic sequence −1, −0.5, 0, 0.5, …

a₁ = −1d = 0.5n = 10
S10 =
2.Easy
kak​135791113ε = 0.05

A ball is dropped and its first rebound reaches 20 m. Every next rebound reaches 60% of the previous one. Which rebound n is the first one lower than 0.05 m?

a₁ = 20r = 0.6ε = 0.05
n =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k³·3ᵏ/4ᵏ. Find L = lim |ak+1/ak|.

ak = k³·3ᵏ/4ᵏ
L =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 1)).

ak = 3/(k(k + 1))
S =
5.Hard

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

ak = (−1)ᵏ/(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 0.0001.

f(x) = cos xx = 1M = 1ε = 0.0001
n =

Answer key

  1. 1. S10 = 12.5
  2. 2. n = 13
  3. 3. L = 0.75
  4. 4. S = 3
  5. 5. S = 0.5403
  6. 6. n = 7

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