PreCalc

Solve:

(x-1)/(x)+(x-2)/(x)+(x-3)/(x)+...+(1)/(x)=3;

X belongs to N

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  1. 3 x = n x - (1+2+3 ...... n)

    1+2+3....+n is arithmetic sequence
    https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html

    a = 1 and d = 1
    sum = (n/2)(2 + n-1)= (n/2)(1+n)
    = .5(n^2+n)
    so
    3x = nx -.5(n^2+n)

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