instead of 20 pts , i will give u 20 salutes................
now , c'mon , gimme the proof................
1/(x+1) >= 3
(3x - 4)/(x-1) <=0
or x lies in (1,4/3] (upper bound(4/3) is the root of numerator and lower bound(1) is root of denominator)
1/(x-1) + 2/(x-2) >=3 implies
(3x2 - 11x +9)/(x-1)(x-2) <=0
or x lies in (1, (11 - 13)/6 )(2, (11 + 13)/6 )
notice that again lower bounds and upper bounds form roots of numerator and denominator respectively.
you will find a similar case for
1/(x-1) + 2/(x-2) + 3/(x-3) >=3
where lower and upper bounds form the roots.
therefore , for 1/(x-1) + 2/(x-2) + 3/(x-3) ....... 120/(x-120) >=3
the roots of numerator and denominator of the simplified expression will give upper and lower bounds.
What is asked is the sum of the roots of the numerator - sum of roots of denominator.
which you can easily find to be 2420.
That solves the problem!
the roots of the denominator will o
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