Posted by Anonymous on Thursday, January 3, 2013 at 10:20am.
Consider the sequence
1,2, 3,4, 5, 6,.........., n(1)^(n+1)
What is the average of first 300 terms of the sequence?

maths  Steve, Thursday, January 3, 2013 at 10:27am
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
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