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Consider the sequence (1/n^2)+(2/n^2)+...+(n/n^2).

What is the limit of the sequence?

  • Math -

    1/n2 ( 1+2+3+...+ n)
    =1/n^2 (n)(n+1)/2=1/n^2(n^2+n)/2
    = (1+1/n)/2

    check it. Let n=5
    sum= 1/25 * (1+2+3+4+5)=15/25=3/5
    by the formula, sum= 1/2 (1+1/5)=3/5

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