• Got a question on how to use our new website? Check out our user guide here!

Strange Induction (1 Viewer)

fan96

617 pages
Joined
May 25, 2017
Messages
441
Location
NSW
Gender
Male
HSC
2018
Have you tried expanding and rearranging?
 

Drongoski

Well-Known Member
Joined
Feb 22, 2009
Messages
3,777
Gender
Male
HSC
N/A
this expression = k3 + 3k2 + 3k ++ 1 + 5k + 5

= (k3 + 5k) + 3k(k+1) + 6

= 6M + 6 + 3k(k+1) (M an integer)

But k(k+1) is always even, since if k is even, then it is; if k is odd, then k+1 is even. .: k(k+1) = 2N (N integer)

.: the original expression becomes 6(M + 1 + N) = 6 x integer.
 
Last edited:

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top