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 = 0.01

A ball is dropped and its first rebound reaches 10 m. Every next rebound reaches 75% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 10r = 0.75ε = 0.01
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 2·(−2/3)ᵏ.

a = 2r = −2/3k₀ = 0
S =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = 2ᵏ·k!/kᵏ
L =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·8ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·8ᵏ/(2k)!
L =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 2 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₂|.

f(x) = sin xn = 2x = 0.8M = 1
|R₂| =
6.Hard

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

ak = 2ᵏ/k!
S =

Answer key

  1. 1. n = 26
  2. 2. S = 1.2
  3. 3. L = 0.7358
  4. 4. L = 2
  5. 5. |R₂| = 0.08533
  6. 6. S = 7.389

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