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 0.5, 0.75, 1.125, …

a₁ = 0.5r = 1.5n = 6
S6 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 8·(3/4)ᵏ.

a = 8r = 3/4k₀ = 1
S =
3.Medium
AΣ (2/3)ᵏk = 1 … ∞BΣ (−1)ᵏ/√kk = 1 … ∞CΣ 1/(2ᵏ + k)k = 1 … ∞DΣ 2ᵏ/k³k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (2/3)ᵏB: Σ (−1)ᵏ/√kC: Σ 1/(2ᵏ + k)D: Σ 2ᵏ/k³
  1. 1A: Σ (2/3)ᵏ
  2. 2B: Σ (−1)ᵏ/√k
  3. 3C: Σ 1/(2ᵏ + k)
  4. 4D: Σ 2ᵏ/k³
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 4)).

ak = 1/(k(k + 4))
S =
5.Hard
xyfP₂0.5

Use the Maclaurin polynomial of degree 2 of f(x) = cos(2x) to approximate f(0.5). Give P₂(0.5).

f(x) = cos(2x)n = 2x = 0.5
P₂(0.5) =
6.Hard

f(x) = eˣ is approximated at x = 1 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 3, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = eˣx = 1M = 3ε = 1 × 10⁻⁶
n =

Answer key

  1. 1. S6 = 10.39
  2. 2. S = 24
  3. 3. D: Σ 2ᵏ/k³
  4. 4. S = 0.5208
  5. 5. P₂(0.5) = 0.5
  6. 6. n = 9

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