Induksi matematika Buktikanlah: 1+5+9+...+(4n-3)=n(2n-1) Mohon jawaban dan caranya

jawab

1+ 5 + 9 + ...+(4n-3) = n (2n -1)

n = 1
(4n-3) = n(2n-1)
1 = 1

n = k
1+5+9 + ...+(4k-3) =  k(2k -1)

n = k + 1
{1 + 5 + 9 + ..(4k -3)} + {4(k+1) - 3} = (k+1){ 2(k+1) - 1}
k (2k - 1) + 4(k+1) - 3 = (k+1) (2k + 2 - 1)
2k² - k + 4k + 4 - 3 = (k+1)(2k +1)
2k² + 3k + 1 = (k+1)(2k +1)
(k + 1)(2k + 1)  = (k + 1)(2k + 1)