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k²/(k²-100k+5000) +(100-k)²/[(100-k)²-100(100-k)+5000]
=k²/(k²-100k+5000)+(k-100)²/(k²-200k+10000-10000+100k+5000)
=k²/(k²-100k+5000)+(k-100)²/(k²-100k+5000)
=[k²+(k-100)²]/(k²-100k+5000)
=(k²+k²-200k+10000)/(k²-100k+5000)
=(2k²-200k+10000)/(k²-100k+5000)
=2(k²-100k+5000)/(k²-100k+5000)
=2
1²/(1²-100+5000)+2²/(2²-200+5000)+...+ 98²/(98²-9800+5000)+99²/(99²-9900+5000)
=[1²/(1²-100+5000)+99²/(99²-9900+5000)]+[2²/(2²-200+5000)+98²/(98²-9800+5000)]
+...+[49²/(49²-4900+5000)+51²/(51²-5100+5000)]+50²/(50²-5000+5000)
=2×49+ 1
=99
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谢谢
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