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^2-n

= -n

so, the average is -n/2n = -1/2

or, rearrange to see that the first 2n terms are

(1-2)+(3-4)+...+(n-(n+1))

= -1 + -1 + ...

= -n

average is -n/2n = -1/2

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