A MATHS 難題, 請高手幫忙解題!

For n=1,
2(1)3+(1)=3,which is divisible by 3.
∴The statement is true for n=1.
Let 2(k)3+(k)= 3A ,where k and A are positive integers.
For n=k+1,
= 2(k+1)3+(k+1)
=2(k3+3k2+3k+1)+(k+1)
=2k3+k+6k2+6k+3
= 3A +6k2+6k+3
=3(A+2k2+2k+1)
∴2(k+1)3+(k+1)is also divisible by 3.
∴The statement is also true for n=k+1 if it is true for n=k.
By the principle of mathematical induction,the statement is true for all positive integer n.

頭果d我唔做了

2k^3+k = 3M

when n=k+1

2(k+1)^3+(k+1)

2(k^3+3k^2+3k+1) + (k+1)

2k^3+6k^2+6k+2+k+1

2k^3 + k +6k^2 + 6k +3

if 2k^3+k = 3M

so 3M+6k^2+6k+3

3(M+2k^2+2k+1)

by pinciple of MI , P(n) is true for all nature number n.