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=2∞ 5·(2/5)ᵏ.

a = 5r = 2/5k₀ = 2
S =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 5·(−3/4)ᵏ.

a = 5r = −3/4k₀ = 0
S =
3.Medium
AΣ k²/5ᵏk = 1 … ∞BΣ 2/kk = 1 … ∞CΣ 1/(k(k + 1))k = 1 … ∞DΣ (3/4)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ k²/5ᵏB: Σ 2/kC: Σ 1/(k(k + 1))D: Σ (3/4)ᵏ
  1. 1A: Σ k²/5ᵏ
  2. 2B: Σ 2/k
  3. 3C: Σ 1/(k(k + 1))
  4. 4D: Σ (3/4)ᵏ
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ kᵏ/(2ᵏ·k!). Find L = lim |ak+1/ak|.

ak = kᵏ/(2ᵏ·k!)
L =
5.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 5 at x = −0.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = cos xn = 5x = −0.5M = 1
|R₅| =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.25ᵏ/k.

ak = (−1)k+1·0.25ᵏ/k
S =

Answer key

  1. 1. S = 1.333
  2. 2. S = 2.857
  3. 3. B: Σ 2/k
  4. 4. L = 1.359
  5. 5. |R₅| = 2.17 × 10⁻⁵
  6. 6. S = 0.2231

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