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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 9·(3/4)ᵏ.

a = 9r = 3/4k₀ = 1
S =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 24·(−3/4)ᵏ.

a = 24r = −3/4k₀ = 1
S =
3.Medium
AΣ 5/kk = 1 … ∞BΣ 1/k⁴k = 1 … ∞CΣ (4/3)ᵏk = 1 … ∞DΣ 2ᵏ/k³k = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 5/kB: Σ 1/k⁴C: Σ (4/3)ᵏD: Σ 2ᵏ/k³
  1. 1A: Σ 5/k
  2. 2B: Σ 1/k⁴
  3. 3C: Σ (4/3)ᵏ
  4. 4D: Σ 2ᵏ/k³
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ kᵏ/(5ᵏ·k!). Find L = lim |ak+1/ak|.

ak = kᵏ/(5ᵏ·k!)
L =
5.Hard

f(x) = sin 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) = sin xn = 3x = 0.5M = 1
|R₃| =
6.Hard
xyfP₄1

Use the Maclaurin polynomial of degree 4 of f(x) = e2x to approximate f(1). Give P₄(1).

f(x) = e2xn = 4x = 1
P₄(1) =

Answer key

  1. 1. S = 27
  2. 2. S = −10.29
  3. 3. B: Σ 1/k⁴
  4. 4. L = 0.5437
  5. 5. |R₃| = 0.002604
  6. 6. P₄(1) = 7

Full step-by-step solutions: practise this topic on examproblems.com.