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 S22 of the first 22 terms of the arithmetic sequence −7, −9, −11, −13, …

a₁ = −7d = −2n = 22
S22 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 3·(1/3)ᵏ.

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

Exactly one of the four series diverges. Click it.

A: Σ 2ᵏ/k³B: Σ (−1)ᵏ/√kC: Σ (3/4)ᵏD: Σ 3/k³
  1. 1A: Σ 2ᵏ/k³
  2. 2B: Σ (−1)ᵏ/√k
  3. 3C: Σ (3/4)ᵏ
  4. 4D: Σ 3/k³
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 6/(k(k + 3)).

ak = 6/(k(k + 3))
S =
5.Hard

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

ak = (−1)k+1/k
S =
6.Hard

f(x) = cos x is approximated at x = 1 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 0.0001.

f(x) = cos xx = 1M = 1ε = 0.0001
n =

Answer key

  1. 1. S22 = −616
  2. 2. S = 0.5
  3. 3. A: Σ 2ᵏ/k³
  4. 4. S = 3.667
  5. 5. S = 0.6931
  6. 6. n = 7

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