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​1234567891011

Find the sum S11 of the first 11 terms of the arithmetic sequence 1, 7, 13, 19, …

a₁ = 1d = 6n = 11
S11 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 18·(−1/4)ᵏ.

a = 18r = −1/4k₀ = 1
S =
3.Medium
AΣ (2/3)ᵏk = 1 … ∞BΣ 1/(k(k + 1))k = 1 … ∞CΣ 1/√kk = 1 … ∞DΣ 2ᵏ/k!k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (2/3)ᵏB: Σ 1/(k(k + 1))C: Σ 1/√kD: Σ 2ᵏ/k!
  1. 1A: Σ (2/3)ᵏ
  2. 2B: Σ 1/(k(k + 1))
  3. 3C: Σ 1/√k
  4. 4D: Σ 2ᵏ/k!
4.Medium
kSn​12345678910

Find the sum S = Σk=137 3/(k(k + 1)).

ak = 3/(k(k + 1))n = 37
S =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.2ᵏ.

ak = k·0.2ᵏ
S =
6.Hard

f(x) = cos x is approximated at x = 0.5 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 0.0005.

f(x) = cos xx = 0.5M = 1ε = 0.0005
n =

Answer key

  1. 1. S11 = 341
  2. 2. S = −3.6
  3. 3. C: Σ 1/√k
  4. 4. S = 2.921
  5. 5. S = 0.3125
  6. 6. n = 4

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