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
kak​135791113ε = 0.5

A ball is dropped and its first rebound reaches 10 m. Every next rebound reaches 75% of the previous one. Which rebound n is the first one lower than 0.5 m?

a₁ = 10r = 0.75ε = 0.5
n =
2.Easy
kak​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 1, 3, 9, …

a₁ = 1r = 3n = 7
S7 =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ (2k)!·xᵏ/(k!)².

Σ (2k)!·xᵏ/(k!)²x₀ = 0
R =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k!/kᵏ. Find L = lim |ak+1/ak|.

ak = k!/kᵏ
L =
5.Hard
xyfP₄0.5

Use the Maclaurin polynomial of degree 4 of f(x) = 1/(1 − x) to approximate f(0.5). Give P₄(0.5).

f(x) = 1/(1 − x)n = 4x = 0.5
P₄(0.5) =
6.Hard

f(x) = cos x is approximated at x = 1 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 0.0005.

f(x) = cos xx = 1M = 1ε = 0.0005
n =

Answer key

  1. 1. n = 12
  2. 2. S7 = 1093
  3. 3. R = 0.25
  4. 4. L = 0.3679
  5. 5. P₄(0.5) = 1.938
  6. 6. n = 6

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