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​13579111315ε = 0.1

A ball is dropped and its first rebound reaches 3 m. Every next rebound reaches 80% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 3r = 0.8ε = 0.1
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 10·(−3/4)ᵏ.

a = 10r = −3/4k₀ = 2
S =
3.Medium
AΣ (−1)ᵏ/kk = 1 … ∞BΣ k/3ᵏk = 1 … ∞CΣ 3ᵏ/k³k = 1 … ∞DΣ (4/5)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (−1)ᵏ/kB: Σ k/3ᵏC: Σ 3ᵏ/k³D: Σ (4/5)ᵏ
  1. 1A: Σ (−1)ᵏ/k
  2. 2B: Σ k/3ᵏ
  3. 3C: Σ 3ᵏ/k³
  4. 4D: Σ (4/5)ᵏ
4.Medium
kSn​12345678910

Find the sum S = Σk=112 12/(k(k + 1)).

ak = 12/(k(k + 1))n = 12
S =
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 4 at x = −0.5. 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 = −0.5M = 1
|R₄| =
6.Hard

f(x) = ln(1 + x) is approximated by its Maclaurin polynomial of degree 2 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 2! = 2 to find the largest possible error |R₂|.

f(x) = ln(1 + x)n = 2x = 0.3M = 2
|R₂| =

Answer key

  1. 1. n = 17
  2. 2. S = 3.214
  3. 3. C: Σ 3ᵏ/k³
  4. 4. S = 11.08
  5. 5. |R₄| = 0.0002604
  6. 6. |R₂| = 0.009

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