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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 4, −12, 36, …

a₁ = 4r = −3n = 7
S7 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 6·(−1/4)ᵏ.

a = 6r = −1/4k₀ = 0
S =
3.Medium
xx₀ = −2??R

The power series Σk=1∞ k²·5ᵏ·(x + 2)ᵏ converges on an interval around x₀ = −2. Find the right end x of that interval.

Σ k²·5ᵏ·(x + 2)ᵏx₀ = −2
x =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k²·5ᵏ/3ᵏ. Find L = lim |ak+1/ak|.

ak = k²·5ᵏ/3ᵏ
L =
5.Hard

f(x) = sin 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) = sin xx = 0.5M = 1ε = 0.0005
n =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ (−1)ᵏ·22k+1/(2k + 1)!.

ak = (−1)ᵏ·22k+1/(2k + 1)!
S =

Answer key

  1. 1. S7 = 2188
  2. 2. S = 4.8
  3. 3. x = −1.8
  4. 4. L = 1.667
  5. 5. n = 4
  6. 6. S = 0.9093

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