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

Find the sum S of the infinite series Σ_k=1^∞ 12·(1/4)ᵏ.

a = 12r = 1/4k₀ = 1

S =

2.Easy

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

a = 10r = 1/2k₀ = 1

S =

3.Medium

Find the sum S = Σ_k=1²⁶ 12/(k(k + 1)).

a_k = 12/(k(k + 1))n = 26

S =

4.Medium

Find the radius of convergence R of the power series Σ_k=1^∞ 3ᵏ·xᵏ/(k + 1).

Σ 3ᵏ·xᵏ/(k + 1)x₀ = 0

R =

5.Hard

f(x) = cos x 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 = 1, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = cos xx = 0.5M = 1ε = 1 × 10⁻⁶

n =

6.Hard

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

a_k = k·(−0.5)ᵏ

S =

Answer key

1. S = 4
2. S = 10
3. S = 11.56
4. R = 0.3333
5. n = 7
6. S = −0.2222

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