Induction (1 Viewer)

[Dreamerish*~]

Prove by induction that:

n³ + (n + 1)³ + (n + 2)³

... is divisble by 9.

Thanks.

 

[acmilan]

Assume n = k is true

k³ + (k + 1)³ + (k + 2)³ = 9M

For n = k+1


(k + 1)³ + (k + 2)³ + (k + 3)³
= 9M - k³ + (k + 3)³
= 9M - k³ + k³ + 9k² + 27k + 27
= 9M - 9k² + 27k + 27
= 9(M - k² + 3k + 3)
= 9N