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.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

The geometric sequence aₙ = 20·0.9ⁿ⁻¹ decreases. Find the first index n for which aₙ < 0.05.

a₁ = 20r = 0.9ε = 0.05

n =

2.Easy

Find the sum S of the infinite series Σ_k=1^∞ 6·(1/3)ᵏ.

a = 6r = 1/3k₀ = 1

S =

3.Medium

Apply the ratio test to Σ_k=1^∞ k!/kᵏ. Find L = lim |a_k+1/a_k|.

a_k = k!/kᵏ

L =

4.Medium

Find the sum S = Σ_k=1^∞ 5/(k(k + 4)).

a_k = 5/(k(k + 4))

S =

5.Hard

Recognise the series and find its sum: S = Σ_k=1^∞ k·(−0.5)ᵏ.

a_k = k·(−0.5)ᵏ

S =

6.Hard

f(x) = eˣ is approximated at x = 0.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 2, find the smallest degree n that guarantees an error below 0.0005.

f(x) = eˣx = 0.5M = 2ε = 0.0005

n =

Answer key

1. n = 58
2. S = 3
3. L = 0.3679
4. S = 2.604
5. S = −0.2222
6. n = 5

Full step-by-step solutions: practise this topic on examproblems.com.