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^∞ 18·(3/4)ᵏ.

a = 18r = 3/4k₀ = 1

S =

2.Easy

Find the sum S₁₀ of the first 10 terms of the geometric sequence 1, −2, 4, …

a₁ = 1r = −2n = 10

S₁₀ =

3.Medium

Apply the ratio test to Σ_k=1^∞ k³·3ᵏ/5ᵏ. Find L = lim |a_k+1/a_k|.

a_k = k³·3ᵏ/5ᵏ

L =

4.Medium

Find the radius of convergence R of the power series Σ_k=1^∞ xᵏ/(k²·3ᵏ).

Σ xᵏ/(k²·3ᵏ)x₀ = 0

R =

5.Hard

Find the coefficient c₃ of (x + 1)³ in the Taylor series of f(x) = e^3x about a = −1.

f(x) = e^3xa = −1k = 3

c₃ =

6.Hard

Use the Maclaurin polynomial of degree 2 of f(x) = cos x to approximate f(1). Give P₂(1).

f(x) = cos xn = 2x = 1

P₂(1) =

Answer key

1. S = 54
2. S₁₀ = −341
3. L = 0.6
4. R = 3
5. c₃ = 0.224
6. P₂(1) = 0.5

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