1^/(1^-100+5000)+2^/(2^-2*100+5000)+...+99^/(99^-99*100+5000)
=1^/(5000-1*99)+2^/(5000-2*98)+...+99^/(5000-99*1)
=(1^+99^)/(5000-1*99)+...+(49^+51^)/(5000-49*50)+50^/(5000-50^)
=2+2+...+1
=2*49+1
=99
[a^+(100-a)]/[5000-a(100-a)]=[2a^-200a+10000]/[5000-100+a^]=2
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