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∞ 12·(−2/3)ᵏ.

a = 12r = −2/3k₀ = 2
S =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 0.5, 0.6, 0.72, …

a₁ = 0.5r = 1.2n = 9
S9 =
3.Medium
xx₀ = 1??R

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

Σ (1/2)ᵏ·(x − 1)ᵏ/(k + 1)x₀ = 1
R =
4.Medium
xx₀ = 3??R

The power series Σk=1∞ k·2ᵏ·(x − 3)ᵏ converges on an interval around x₀ = 3. Find the right end x of that interval.

Σ k·2ᵏ·(x − 3)ᵏx₀ = 3
x =
5.Hard

Find the coefficient c₂ of (x − 2)² in the Taylor series of f(x) = e2x about a = 2.

f(x) = e2xa = 2k = 2
c₂ =
6.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 3 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 3! = 6 to find the largest possible error |R₃|.

f(x) = ln(1 + x)n = 3x = 0.2M = 6
|R₃| =

Answer key

  1. 1. S = 3.2
  2. 2. S9 = 10.4
  3. 3. R = 2
  4. 4. x = 3.5
  5. 5. c₂ = 109.2
  6. 6. |R₃| = 0.0004

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