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 2 m. Every next rebound reaches 80% of the previous one. Which rebound n is the first one lower than 0.01 m?

a₁ = 2r = 0.8ε = 0.01
n =
2.Easy
kak​13579111315ε = 0.1

The geometric sequence aₙ = 2·0.8ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.1.

a₁ = 2r = 0.8ε = 0.1
n =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 6/(k(k + 4)).

ak = 6/(k(k + 4))
S =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 25ᵏx²ᵏ/k.

Σ 25ᵏx²ᵏ/kx₀ = 0
R =
5.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 5 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e1.5 = 4.482 to find the largest possible error |R₅|.

f(x) = eˣn = 5x = 1.5M = 4.482
|R₅| =
6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 5 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = sin xn = 5x = 0.3M = 1
|R₅| =

Answer key

  1. 1. n = 25
  2. 2. n = 15
  3. 3. S = 3.125
  4. 4. R = 0.2
  5. 5. |R₅| = 0.0709
  6. 6. |R₅| = 1.012 × 10⁻⁶

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