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​1234567

Find the sum S7 of the first 7 terms of the geometric sequence 5, −10, 20, …

a₁ = 5r = −2n = 7
S7 =
2.Easy
kak​12345678

Find the sum S8 of the first 8 terms of the geometric sequence 2, 2.4, 2.88, …

a₁ = 2r = 1.2n = 8
S8 =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 16ᵏx²ᵏ/k.

Σ 16ᵏx²ᵏ/kx₀ = 0
R =
4.Medium
AΣ 1/(k(k + 1))k = 1 … ∞BΣ (3/5)ᵏk = 1 … ∞CΣ ln k / kk = 1 … ∞DΣ 2/k⁴k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/(k(k + 1))B: Σ (3/5)ᵏC: Σ ln k / kD: Σ 2/k⁴
  1. 1A: Σ 1/(k(k + 1))
  2. 2B: Σ (3/5)ᵏ
  3. 3C: Σ ln k / k
  4. 4D: Σ 2/k⁴
5.Hard

f(x) = eˣ is approximated at x = 1 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 3, find the smallest degree n that guarantees an error below 0.0005.

f(x) = eˣx = 1M = 3ε = 0.0005
n =
6.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 2 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₂|.

f(x) = cos xn = 2x = 0.8M = 1
|R₂| =

Answer key

  1. 1. S7 = 215
  2. 2. S8 = 33
  3. 3. R = 0.25
  4. 4. C: Σ ln k / k
  5. 5. n = 7
  6. 6. |R₂| = 0.08533

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