Question

If the nth term of a sequnce be tn=(n-1) (n-2) (n-3), then show that the first terms is zero, but the rest of the term are positive

Answer 1

I believe the question says first three terms are zeros and the rest are positive.
Given nth term is
$(n - 1)(n - 2)(n - 3)$
Now for this to be positive,
$(n - 1)(n - 2)(n - 3) > 0 \\ (n - 1) > 0 \: or \: (n - 2) > 0 \: or \: (n - 3) > 0 \\ n > 1 \: or \: n > 2 \: or \: n > 3$
Now since its or statement, we can take n>3.
This implies that the nth term will be positive if n>3.
Now to prove first three terms are zeros, put n=1 , n=2, and n=3 and you will get nth term = 0
Hope this helps.