1+1/1*2*3+1/2*3*4+1/3*4*5+.+1/98*99*100=

楼上的错了
1+1/1*2*3+1/2*3*4+1/3*4*5+.+1/98*99*100
=1+1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+1/2*(1/3*4-1/4*5)+.+1/2*(1/98*99-1/99*100)
=1+1/2*(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+.+1/98*99-1/99*100)
=1+1/2*(1/1*2-1/99*100)
=1+1/2*4949/9900
=1又4949/19800

an=1/2n+1/2(n+2)-1/(n+1)
1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100
=(1/2+1/6-1/2)+(1/4+1/8-1/3)+...+(1/196+1/200-1/99)
=0.5*(1+1/2+...+1/98)+0.5*(1/3+1/4+...+1/100)-(1/2+1/3+1/4+...+1/99)
=0.5*(1+1/2+1/99+1/100)-1/2-1/99
=4949/19800
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