Calculus
posted by Timofey on .
Use mathematical induction to prove that the statement holds for all positive integers. Also, label the basis, hypothesis, and induction step.
1 + 5 + 9 + … + (4n 3)= n(2n1)

for k=1: 1 = 1(21)
assume for k
for n=k+1,
1+5+...+(4k3)+(4(k+1)3) = k(2k1) + (4(k+1)3)
= k(2k1) + (4k+1)
= 2k^2  k + 4k + 1
= 2k^2 + 3k + 1
= (k+1)(2k+1)
= (k+1)(2(k+1)1)