I got in to this problem from Jan 2002 P4 question paper. The problem is that I need to deduce n(n-1)(2n+5) is divisible by 6 for all n>1. How do I deduce this without induction? This question has only 2 marks.
Thanks in advance.
Help! cannot solve P4 problem Watch
- Thread Starter
- 18-12-2010 16:07
- 18-12-2010 16:11
I've not done it properly but you could try to look at what happens when n is odd and even?
- 18-12-2010 16:14
A number is divisible by 6 iff it is divisible both by 2 and 3.
If you consider even n (say 2k) or odd n (2k+1) you should find both work.
Then 3k, 3k+1 and 3k+2 for possibilities modulo 3 ( like odd/even but using 3 )