Mathematics Form4 M2 急問!!(10分)

Mathematics Form4 M2 急問!!!!!!!

1/ 3 + 7 + 11 +…+ (4n-1) = n(2n+1)

2/ 1x0 + 2x1 + 3x2 +…+ n(n-1) = n(n-1) (n+1) / 3

3/ 1²/1.3 + 2²/3.5 + 3²/5.7 + … + n²/(2n-1)(2n+1) = n(n+1)/2(2n+1)

4/ (a) Prove, by mathematical induction, that
1³ + 2³ + 3³ + … + n³ = 1/4 n² (n+1)²
for all positive integers n.

(b) Hence find the value of
2³+ 4³+ 6³+…+30³