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^∞ 24·(3/4)ᵏ.

a = 24r = 3/4k₀ = 1

S =

2.Easy

Find the sum S of the infinite series Σ_k=1^∞ 18·(2/5)ᵏ.

a = 18r = 2/5k₀ = 1

S =

3.Medium

The power series Σ_k=1^∞ k!·(x − 2)ᵏ/kᵏ converges on an interval around x₀ = 2. Find the left end x of that interval.

Σ k!·(x − 2)ᵏ/kᵏx₀ = 2

x =

4.Medium

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

a_k = 3ᵏ·k!/kᵏ

L =

5.Hard

Use the Maclaurin polynomial of degree 2 of f(x) = 1/(1 − 2x) to approximate f(0.25). Give P₂(0.25).

f(x) = 1/(1 − 2x)n = 2x = 0.25

P₂(0.25) =

6.Hard

Find the coefficient c₂ of (x − 1)² in the Taylor series of f(x) = ∛x about a = 1.

f(x) = ∛xa = 1k = 2

c₂ =

Answer key

1. S = 72
2. S = 12
3. x = −0.7183
4. L = 1.104
5. P₂(0.25) = 1.75
6. c₂ = −0.1111

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