maths
posted by Anonymous on .
Consider the sequence
1,2, 3,4, 5, 6,.........., n(1)^(n+1)
What is the average of first 300 terms of the sequence?

rearrange the terms to see that the first 2n terms are
1+3+5+...  2(1+2+3+...)
= n^2  2(n(n+1)/2)
= n^2  n^2n
= n
so, the average is n/2n = 1/2
or, rearrange to see that the first 2n terms are
(12)+(34)+...+(n(n+1))
= 1 + 1 + ...
= n
average is n/2n = 1/2