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∞ 3·(−1/4)ᵏ.

a = 3r = −1/4k₀ = 2
S =
2.Easy
kak​123456789101112

Find the sum S15 of the first 15 terms of the arithmetic sequence −9, −7.5, −6, −4.5, …

a₁ = −9d = 1.5n = 15
S15 =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 2/(k(k + 3)).

ak = 2/(k(k + 3))
S =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ (k!)²·5ᵏ/(2k)!. Find L = lim |ak+1/ak|.

ak = (k!)²·5ᵏ/(2k)!
L =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 4 at x = 1.5. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = sin xn = 4x = 1.5M = 1
|R₄| =
6.Hard

Find the coefficient c₃ of (x − 2)³ in the Taylor series of f(x) = e3x about a = 2.

f(x) = e3xa = 2k = 3
c₃ =

Answer key

  1. 1. S = 0.15
  2. 2. S15 = 22.5
  3. 3. S = 1.222
  4. 4. L = 1.25
  5. 5. |R₄| = 0.06328
  6. 6. c₃ = 1815

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