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​123456789101112

Find the sum S30 of the first 30 terms of the arithmetic sequence −4, −2.5, −1, 0.5, …

a₁ = −4d = 1.5n = 30
S30 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 8·(−1/4)ᵏ.

a = 8r = −1/4k₀ = 2
S =
3.Medium
xx₀ = −2??R

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

Σ (2k)!·(x + 2)ᵏ/(k!)²x₀ = −2
x =
4.Medium
AΣ (k + 3)/k²k = 1 … ∞BΣ (−1)ᵏ/kk = 1 … ∞CΣ (3/2)ᵏk = 1 … ∞DΣ k!/3ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (k + 3)/k²B: Σ (−1)ᵏ/kC: Σ (3/2)ᵏD: Σ k!/3ᵏ
  1. 1A: Σ (k + 3)/k²
  2. 2B: Σ (−1)ᵏ/k
  3. 3C: Σ (3/2)ᵏ
  4. 4D: Σ k!/3ᵏ
5.Hard

Find the coefficient c₂ of (x − 2)² in the Taylor series of f(x) = ln x about a = 2.

f(x) = ln xa = 2k = 2
c₂ =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 2 at x = 0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.5 = 1.649 to find the largest possible error |R₂|.

f(x) = eˣn = 2x = 0.5M = 1.649
|R₂| =

Answer key

  1. 1. S30 = 532.5
  2. 2. S = 0.4
  3. 3. x = −2.25
  4. 4. B: Σ (−1)ᵏ/k
  5. 5. c₂ = −0.125
  6. 6. |R₂| = 0.03435

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