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∞ 10·(−1/2)ᵏ.

a = 10r = −1/2k₀ = 2
S =
2.Easy
kak​123456789101112

Find the sum S20 of the first 20 terms of the arithmetic sequence −11, −10.5, −10, −9.5, …

a₁ = −11d = 0.5n = 20
S20 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 2)).

ak = 3/(k(k + 2))
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 3)).

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

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = e−x about a = 1.

f(x) = e−xa = 1k = 4
c₄ =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 3 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e1.5 = 4.482 to find the largest possible error |R₃|.

f(x) = eˣn = 3x = 1.5M = 4.482
|R₃| =

Answer key

  1. 1. S = 1.667
  2. 2. S20 = −125
  3. 3. S = 2.25
  4. 4. S = 0.6111
  5. 5. c₄ = 0.01533
  6. 6. |R₃| = 0.9454

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