Solutions

  1. Answer:
    1. 24
    2. 6
    3. 3, 7, 15, 31
    4. 1, 4, 9, 16

  2. Answer:
    1. \(\frac{1}{1(1+1)} + \frac{1}{2(2+1)} + \frac{1}{3(3+1)} + ... + \frac{1}{n(n+1)} = \frac{n}{n+1}\)
    2. \(\frac{1}{1(2)} + \frac{1}{2(3)} + \frac{1}{3(4)} = \frac{1}{2} + \frac{1}{6} + \frac{1}{12} = \frac{3}{4} = \frac{3}{3+1}\)
    3. \(1+2^3+3^3 + ... + n^3 = (\frac{1}{4})n^2(n+1)^2 \; \; \; 1+8+27=36=(\frac{1}{4})(3)^2(3+1)^2\)

  3. Answer: \((x+y)^3 = \binom{3}{0}x^3 + \binom{3}{1}x^2y + \binom{3}{2}xy^2 + \binom{3}{3}y^n\)

  4. Answer:
    1. {x ∈ Q | 0 < x ≤ 5}
    2. {x ∈ Q | −5 < x < 5} = B5
    3. ∅
    4. {x ∈ Q | −1 < x < 1} = B1

  5. Answer:
    1. 36
    2. 105