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∞ 10·(1/3)ᵏ.

a = 10r = 1/3k₀ = 2
S =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 2, −1, 0.5, …

a₁ = 2r = −0.5n = 9
S9 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = (k!)²·3ᵏ/(2k)!
L =
4.Medium
xx₀ = 3??R

Find the radius of convergence R of the power series Σk=1∞ (x − 3)ᵏ/5ᵏ.

Σ (x − 3)ᵏ/5ᵏx₀ = 3
R =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.2ᵏ/k.

ak = (−1)k+1·0.2ᵏ/k
S =
6.Hard

Find the coefficient c₄ of (x − 1)⁴ in the Taylor series of f(x) = 1/x about a = 1.

f(x) = 1/xa = 1k = 4
c₄ =

Answer key

  1. 1. S = 1.667
  2. 2. S9 = 1.336
  3. 3. L = 0.75
  4. 4. R = 5
  5. 5. S = 0.1823
  6. 6. c₄ = 1

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