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^∞ 5·(3/4)ᵏ.

a = 5r = 3/4k₀ = 1

S =

2.Easy

Find the sum S of the infinite series Σ_k=1^∞ 6·(−2/3)ᵏ.

a = 6r = −2/3k₀ = 1

S =

3.Medium

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

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

S =

4.Medium

Find the sum S = Σ_k=1²⁰ 12/(k(k + 1)).

a_k = 12/(k(k + 1))n = 20

S =

5.Hard

f(x) = eˣ 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 = 2, find the smallest degree n that guarantees an error below 0.001.

f(x) = eˣx = 0.5M = 2ε = 0.001

n =

6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 4 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = sin xn = 4x = 0.2M = 1

|R₄| =

Answer key

1. S = 15
2. S = −2.4
3. S = 0.6111
4. S = 11.43
5. n = 4
6. |R₄| = 2.667 × 10⁻⁶

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