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 2, 1, 0.5, …

a₁ = 2r = 0.5n = 6
S6 =
2.Easy
kak​123456

Find the sum S6 of the first 6 terms of the geometric sequence 4, 2, 1, …

a₁ = 4r = 0.5n = 6
S6 =
3.Medium
xx₀ = −2??R

The power series Σk=1∞ k·4ᵏ·(x + 2)ᵏ converges on an interval around x₀ = −2. Find the right end x of that interval.

Σ k·4ᵏ·(x + 2)ᵏx₀ = −2
x =
4.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ 4ᵏx²ᵏ/k.

Σ 4ᵏx²ᵏ/kx₀ = 0
R =
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 4 at x = 1. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = cos xn = 4x = 1M = 1
|R₄| =
6.Hard

f(x) = sin x is approximated at x = 1.5 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = sin xx = 1.5M = 1ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. S6 = 3.938
  2. 2. S6 = 7.875
  3. 3. x = −1.75
  4. 4. R = 0.5
  5. 5. |R₄| = 0.008333
  6. 6. n = 11

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