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=0^∞ 10·(−1/4)ᵏ.

a = 10r = −1/4k₀ = 0

S =

2.Easy

Find the sum S₁₅ of the first 15 terms of the arithmetic sequence 8, 14, 20, 26, …

a₁ = 8d = 6n = 15

S₁₅ =

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

Apply the ratio test to Σ_k=1^∞ kᵏ/(3ᵏ·k!). Find L = lim |a_k+1/a_k|.

a_k = kᵏ/(3ᵏ·k!)

L =

5.Hard

Use the Maclaurin polynomial of degree 2 of f(x) = ln(1 + 2x) to approximate f(−0.2). Give P₂(−0.2).

f(x) = ln(1 + 2x)n = 2x = −0.2

P₂(−0.2) =

6.Hard

f(x) = sin 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 0.0005.

f(x) = sin xx = 2M = 1ε = 0.0005

n =

Answer key

1. S = 8
2. S₁₅ = 750
3. L = 0.5437
4. L = 0.9061
5. P₂(−0.2) = −0.48
6. n = 9

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