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^∞ 6·(−1/4)ᵏ.

a = 6r = −1/4k₀ = 1

S =

2.Easy

Find the sum S of the infinite series Σ_k=2^∞ 4·(−2/5)ᵏ.

a = 4r = −2/5k₀ = 2

S =

3.Medium

Find the sum S = Σ_k=1^∞ 12/(k(k + 2)).

a_k = 12/(k(k + 2))

S =

4.Medium

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

a_k = k!/kᵏ

L =

5.Hard

f(x) = cos x is approximated at x = 2 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 0.001.

f(x) = cos xx = 2M = 1ε = 0.001

n =

6.Hard

f(x) = eˣ is approximated at x = 2 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 8, find the smallest degree n that guarantees an error below 0.0005.

f(x) = eˣx = 2M = 8ε = 0.0005

n =

Answer key

1. S = −1.2
2. S = 0.4571
3. S = 9
4. L = 0.3679
5. n = 9
6. n = 10

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