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​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 1, −0.5, 0.25, …

a₁ = 1r = −0.5n = 9
S9 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 12·(−2/3)ᵏ.

a = 12r = −2/3k₀ = 0
S =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

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

ak = 3ᵏ·k!/kᵏ
L =
4.Medium
xx₀ = −1??R

Find the radius of convergence R of the power series Σk=1∞ k²·3ᵏ·(x + 1)ᵏ.

Σ k²·3ᵏ·(x + 1)ᵏx₀ = −1
R =
5.Hard
xyfP₄0.25

Use the Maclaurin polynomial of degree 4 of f(x) = 1/(1 − 2x) to approximate f(0.25). Give P₄(0.25).

f(x) = 1/(1 − 2x)n = 4x = 0.25
P₄(0.25) =
6.Hard

f(x) = eˣ is approximated by its Maclaurin polynomial of degree 5 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = e0.3 = 1.35 to find the largest possible error |R₅|.

f(x) = eˣn = 5x = 0.3M = 1.35
|R₅| =

Answer key

  1. 1. S9 = 0.668
  2. 2. S = 7.2
  3. 3. L = 1.104
  4. 4. R = 0.3333
  5. 5. P₄(0.25) = 1.938
  6. 6. |R₅| = 1.367 × 10⁻⁶

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