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=2∞ 6·(4/5)ᵏ.

a = 6r = 4/5k₀ = 2
S =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 9·(−1/4)ᵏ.

a = 9r = −1/4k₀ = 0
S =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ xᵏ/3ᵏ.

Σ xᵏ/3ᵏx₀ = 0
R =
4.Medium
xx₀ = 3??R

The power series Σk=1∞ 5ᵏ·(x − 3)ᵏ/(k + 1) converges on an interval around x₀ = 3. Find the left end x of that interval.

Σ 5ᵏ·(x − 3)ᵏ/(k + 1)x₀ = 3
x =
5.Hard

Find the coefficient c₂ of (x − 4)² in the Taylor series of f(x) = ln x about a = 4.

f(x) = ln xa = 4k = 2
c₂ =
6.Hard

f(x) = cos x is approximated at x = 0.5 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 0.0005.

f(x) = cos xx = 0.5M = 1ε = 0.0005
n =

Answer key

  1. 1. S = 19.2
  2. 2. S = 7.2
  3. 3. R = 3
  4. 4. x = 2.8
  5. 5. c₂ = −0.03125
  6. 6. n = 4

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