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 S₉ of the first 9 terms of the geometric sequence 0.5, 0.4, 0.32, …

a₁ = 0.5r = 0.8n = 9

S₉ =

3.Medium

Apply the ratio test to Σ_k=1^∞ kᵏ/(5ᵏ·k!). Find L = lim |a_k+1/a_k|.

a_k = kᵏ/(5ᵏ·k!)

L =

4.Medium

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

a_k = 3/(k(k + 1))

S =

5.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 0.0001.

f(x) = eˣx = 2M = 8ε = 0.0001

n =

6.Hard

f(x) = sin 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 0.001.

f(x) = sin xx = 0.5M = 1ε = 0.001

n =

Answer key

1. S = −1.2
2. S₉ = 2.164
3. L = 0.5437
4. S = 3
5. n = 11
6. n = 4

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