Buktikan Rumus berikut dengan Induksi Matematika !

3
1²+3²+5² +...+(2n-1)² = 1/3 (n)(2n-1)(2n+1)
n =1 (b)
n = k ↔1²+3²+5² +...+(2k-1)² = 1/3 (k)(2k-1)(2k+1)
n= k+1 ↔ 1/3 k(2k-1)(2k+1)+ {2(k+1-1)²} = 1/3 (k+1) (2(k+1)-1) (2(k+1) +1)
1/3 k(2k-1)(2k+1) + 4k² = 1/3 (k+1)(2k +1)(2k+3)
1/3 (2k² -k)(2k+1) + 4k² = 1/3 (k+1)(2k+1)(2k+3)
1/3 (4k³- k ) + 4k² = 1/3 (k+1)(2k+1)(2k+3)
1/3 (4k³ - k + 12 k²) = 1/3 (k+1)(2k+1)(2k+3)
1/3 (k+1)(2k+1)(2k+3) = 1/2 (k+1)(2k+1)(2k+3)