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​13579111315ε = 0.1

A ball is dropped and its first rebound reaches 20 m. Every next rebound reaches 85% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 20r = 0.85ε = 0.1
n =
2.Easy
kak​12345678ε = 0.5

A ball is dropped and its first rebound reaches 8 m. Every next rebound reaches 60% of the previous one. Which rebound n is the first one lower than 0.5 m?

a₁ = 8r = 0.6ε = 0.5
n =
3.Medium
xx₀ = 1??R

The power series Σk=1∞ k²·4ᵏ·(x − 1)ᵏ converges on an interval around x₀ = 1. Find the left end x of that interval.

Σ k²·4ᵏ·(x − 1)ᵏx₀ = 1
x =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 1)).

ak = 3/(k(k + 1))
S =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 5 at x = 1. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = sin xn = 5x = 1M = 1
|R₅| =
6.Hard

Find the coefficient c₃ of (x − 3)³ in the Taylor series of f(x) = 1/x about a = 3.

f(x) = 1/xa = 3k = 3
c₃ =

Answer key

  1. 1. n = 34
  2. 2. n = 7
  3. 3. x = 0.75
  4. 4. S = 3
  5. 5. |R₅| = 0.001389
  6. 6. c₃ = −0.01235

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