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​123456

Find the sum S6 of the first 6 terms of the geometric sequence 3, 1.5, 0.75, …

a₁ = 3r = 0.5n = 6
S6 =
2.Easy
kak​13579111315ε = 0.1

A ball is dropped and its first rebound reaches 5 m. Every next rebound reaches 85% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 5r = 0.85ε = 0.1
n =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ 3ᵏ·k!/kᵏ. Find L = lim |ak+1/ak|.

ak = 3ᵏ·k!/kᵏ
L =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 1)).

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

Find the coefficient c₂ of (x − 8)² in the Taylor series of f(x) = ∛x about a = 8.

f(x) = ∛xa = 8k = 2
c₂ =
6.Hard

f(x) = eˣ is approximated at x = 1 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 3, find the smallest degree n that guarantees an error below 0.0001.

f(x) = eˣx = 1M = 3ε = 0.0001
n =

Answer key

  1. 1. S6 = 5.906
  2. 2. n = 26
  3. 3. L = 1.104
  4. 4. S = 3
  5. 5. c₂ = −0.003472
  6. 6. n = 7

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