1+1/2+2/2+3/1+3/2+3/3 100/1+100/2+ +100/100和是多少

问题描述:

1+1/2+2/2+3/1+3/2+3/3 100/1+100/2+ +100/100和是多少
1/1;2/1,2/2;3/1,3/2,3/3;4/1,4/2,4/3,4/4;...,1/100,2/100,...,100/100.这串数的和是多少

1/n+2/n+3/n+……+n/n=[n(n+1)/2]/n=(n+1)/2=n/2+1/2所以原式=(1/2+1/2)+(2/2+1/2)+(3/2+1/2)+……+(100/2+1/2)=(1+2+3+……+100)/2+100*(1/2)=(100*101/2)/2+50=2525+50=2575