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=1∞ 5·(−2/3)ᵏ.

a = 5r = −2/3k₀ = 1
S =
2.Easy
kak​123456789101112

The arithmetic sequence 3, −1, −5, −9, … ends with the term −97. How many terms n does it have?

a₁ = 3d = −4aₙ = −97
n =
3.Medium
xx₀ = 1??R

Find the radius of convergence R of the power series Σk=1∞ (x − 1)ᵏ/2ᵏ.

Σ (x − 1)ᵏ/2ᵏx₀ = 1
R =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 3)).

ak = 3/(k(k + 3))
S =
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

f(x) = cos x is approximated by its Maclaurin polynomial of degree 3 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₃|.

f(x) = cos xn = 3x = 0.5M = 1
|R₃| =

Answer key

  1. 1. S = −2
  2. 2. n = 26
  3. 3. R = 2
  4. 4. S = 1.833
  5. 5. n = 4
  6. 6. |R₃| = 0.002604

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