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March 26, 2017

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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 - ,

    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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