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=0∞ 10·(−1/3)ᵏ.

a = 10r = −1/3k₀ = 0
S =
2.Easy
kak​123456789101112

Find the sum S12 of the first 12 terms of the arithmetic sequence 9, 7, 5, 3, …

a₁ = 9d = −2n = 12
S12 =
3.Medium
AΣ 1/(k(k + 3))k = 1 … ∞BΣ (−1)ᵏ/kk = 1 … ∞CΣ (4/5)ᵏk = 1 … ∞DΣ (4/3)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 1/(k(k + 3))B: Σ (−1)ᵏ/kC: Σ (4/5)ᵏD: Σ (4/3)ᵏ
  1. 1A: Σ 1/(k(k + 3))
  2. 2B: Σ (−1)ᵏ/k
  3. 3C: Σ (4/5)ᵏ
  4. 4D: Σ (4/3)ᵏ
4.Medium
xx₀ = −1??R

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

Σ (2k)!·(x + 1)ᵏ/(k!)²x₀ = −1
R =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 5 at x = 1. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = sin xn = 5x = 1M = 1
|R₅| =
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. S = 7.5
  2. 2. S12 = −24
  3. 3. D: Σ (4/3)ᵏ
  4. 4. R = 0.25
  5. 5. |R₅| = 0.001389
  6. 6. |R₂| = 0.08533

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