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=1∞ 9·(1/4)ᵏ.

a = 9r = 1/4k₀ = 1
S =
2.Easy
kak​123456789ε = 0.1

A ball is dropped and its first rebound reaches 8 m. Every next rebound reaches 50% of the previous one. Which rebound n is the first one lower than 0.1 m?

a₁ = 8r = 0.5ε = 0.1
n =
3.Medium
AΣ 3ᵏ/k²k = 1 … ∞BΣ k²/5ᵏk = 1 … ∞CΣ (−1)ᵏ/kk = 1 … ∞DΣ (4/5)ᵏk = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ 3ᵏ/k²B: Σ k²/5ᵏC: Σ (−1)ᵏ/kD: Σ (4/5)ᵏ
  1. 1A: Σ 3ᵏ/k²
  2. 2B: Σ k²/5ᵏ
  3. 3C: Σ (−1)ᵏ/k
  4. 4D: Σ (4/5)ᵏ
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k²·2ᵏ/3ᵏ. Find L = lim |ak+1/ak|.

ak = k²·2ᵏ/3ᵏ
L =
5.Hard
xyfP₂1.2

Use the Maclaurin polynomial of degree 2 of f(x) = cos x to approximate f(1.2). Give P₂(1.2).

f(x) = cos xn = 2x = 1.2
P₂(1.2) =
6.Hard

Recognise the series and find its sum: S = Σk=0∞ 2ᵏ/k!.

ak = 2ᵏ/k!
S =

Answer key

  1. 1. S = 3
  2. 2. n = 8
  3. 3. A: Σ 3ᵏ/k²
  4. 4. L = 0.6667
  5. 5. P₂(1.2) = 0.28
  6. 6. S = 7.389

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