So the question was basically " Suppose that there are n teams in a rugby league competition. Every team A plays every other team B twice, once at the home ground for team A, and the other time at the home ground for team B."
2(n 1) + 2(n 2) + 2(n 3) + : : : + 6 + 4 + 2 is given
a) Write the expression in summation notation. b) Use mathematical induction to prove it, n>=2
So I got this expression for (a) n^Sigma(i=1) = (2(n-i)) where n is the number of teams
Let P(n) denote the sequence n^Sigma(i=1)=2(n-i) and n≥2
Consider P (2) n^Sigma(i=1)=2(n-i) =2(2-1)=2 ∴it is true when n=2
We will now assume it is true for P(k)
k^Sigma(i=1)=2(k-i) for some integer k ≥2
k+1^Sigma(i=1)=2(k+1-i) for some integer k ≥2
Since we have assumed that P(k) is true.
So we know: P(k+1)=P(k)+(k+1)
ANSWER i cant answer my own question for 8hrs so here it is:
Therefore under induction the sequence has been proven.
Thanks to @P..