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

Find the sum S of the infinite series Σ_k=1^∞ 10·(2/5)ᵏ.

a = 10r = 2/5k₀ = 1

S =

2.Easy

Find the sum S of the infinite series Σ_k=2^∞ 4·(1/2)ᵏ.

a = 4r = 1/2k₀ = 2

S =

3.Medium

Find the sum S = Σ_k=1^∞ 3/(k(k + 2)).

a_k = 3/(k(k + 2))

S =

4.Medium

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

Σ 25ᵏx²ᵏ/kx₀ = 0

R =

5.Hard

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

f(x) = cos xn = 5x = 1M = 1

|R₅| =

6.Hard

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

a_k = (−1)ᵏ·2^2k/(2k)!

S =

Answer key

1. S = 6.667
2. S = 2
3. S = 2.25
4. R = 0.2
5. |R₅| = 0.001389
6. S = −0.4161

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