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​123456

Find the sum S6 of the first 6 terms of the geometric sequence 1, 1.2, 1.44, …

a₁ = 1r = 1.2n = 6
S6 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 2·(−1/2)ᵏ.

a = 2r = −1/2k₀ = 0
S =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k³·4ᵏ/3ᵏ. Find L = lim |ak+1/ak|.

ak = k³·4ᵏ/3ᵏ
L =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ 2ᵏ·k!/kᵏ. Find L = lim |ak+1/ak|.

ak = 2ᵏ·k!/kᵏ
L =
5.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 2 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 2! = 2 to find the largest possible error |R₂|.

f(x) = ln(1 + x)n = 2x = 0.2M = 2
|R₂| =
6.Hard

Find the coefficient c₃ of (x − 1)³ in the Taylor series of f(x) = ∛x about a = 1.

f(x) = ∛xa = 1k = 3
c₃ =

Answer key

  1. 1. S6 = 9.93
  2. 2. S = 1.333
  3. 3. L = 1.333
  4. 4. L = 0.7358
  5. 5. |R₂| = 0.002667
  6. 6. c₃ = 0.06173

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