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∞ 18·(−2/3)ᵏ.

a = 18r = −2/3k₀ = 2
S =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 24·(−1/3)ᵏ.

a = 24r = −1/3k₀ = 2
S =
3.Medium
kSn​12345678910

Find the sum S = Σk=135 1/(k(k + 1)).

ak = 1/(k(k + 1))n = 35
S =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 3/(k(k + 2)).

ak = 3/(k(k + 2))
S =
5.Hard

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

f(x) = √xa = 4k = 2
c₂ =
6.Hard
xyfP₄0.25

Use the Maclaurin polynomial of degree 4 of f(x) = 1/(1 − 2x) to approximate f(0.25). Give P₄(0.25).

f(x) = 1/(1 − 2x)n = 4x = 0.25
P₄(0.25) =

Answer key

  1. 1. S = 4.8
  2. 2. S = 2
  3. 3. S = 0.9722
  4. 4. S = 2.25
  5. 5. c₂ = −0.01563
  6. 6. P₄(0.25) = 1.938

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