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
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 2·(1/3)ᵏ.

a = 2r = 1/3k₀ = 1
S =
2.Easy
kak​123456789101112

Find the sum S36 of the first 36 terms of the arithmetic sequence 11, 17, 23, 29, …

a₁ = 11d = 6n = 36
S36 =
3.Medium
kSn​12345678910

Find the sum S = Σk=130 2/(k(k + 1)).

ak = 2/(k(k + 1))n = 30
S =
4.Medium
xx₀ = 3??R

The power series Σk=1∞ k!·(x − 3)ᵏ/kᵏ converges on an interval around x₀ = 3. Find the left end x of that interval.

Σ k!·(x − 3)ᵏ/kᵏx₀ = 3
x =
5.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 0.0001.

f(x) = sin xx = 2M = 1ε = 0.0001
n =
6.Hard
xyfP₃0.5

Use the Maclaurin polynomial of degree 3 of f(x) = 1/(1 − x) to approximate f(0.5). Give P₃(0.5).

f(x) = 1/(1 − x)n = 3x = 0.5
P₃(0.5) =

Answer key

  1. 1. S = 1
  2. 2. S36 = 4176
  3. 3. S = 1.935
  4. 4. x = 0.2817
  5. 5. n = 10
  6. 6. P₃(0.5) = 1.875

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