buktikanlah dengan induksi matematika : 2 + 4 + 6 + 8 + 10 + 12 + 14 + ............. +2n = n2 + n

jawab
2+4+6+...+2n =  n²+n

n =1 → 2n  = n²+n (B)
n = k → 2+4+6+...+2k = k² + k (B)

n = k+1
{2+4+6+...+ 2k}+ 2(k+1) = (k+1)² +(k+1)
k² + k + 2k + 2 = (k+1)² + (k+1)
(k² + 2k  + 1 ) +(k+1) = (k+1)² + (k+1)
(k+1)² + (k+1) = (k+1)² + (k+1)