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∞ 3·(−1/2)ᵏ.

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

Find the sum S24 of the first 24 terms of the arithmetic sequence −7, −4, −1, 2, …

a₁ = −7d = 3n = 24
S24 =
3.Medium
xx₀ = −2??R

Find the radius of convergence R of the power series Σk=1∞ k·2ᵏ·(x + 2)ᵏ.

Σ k·2ᵏ·(x + 2)ᵏx₀ = −2
R =
4.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((3k + 3)/(5k + 4))ᵏ. Find L = lim |ak|1/k.

ak = ((3k + 3)/(5k + 4))ᵏ
L =
5.Hard

f(x) = cos x is approximated at x = 1.5 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 1 × 10⁻⁶.

f(x) = cos xx = 1.5M = 1ε = 1 × 10⁻⁶
n =
6.Hard
xyfP₂0.25

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) =

Answer key

  1. 1. S = −1
  2. 2. S24 = 660
  3. 3. R = 0.5
  4. 4. L = 0.6
  5. 5. n = 11
  6. 6. P₂(0.25) = 1.75

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