1+1+2分之1+1+2+3分之1+1+2+3+4分之1…………+1+2+3+4…+100分之1 怎么算额?

1+2+3+4+。+n=(1+n)*n/21+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+。+1/(12+3+。+100)=1+1/[(1*2)/2]+1/[(2*3)/2]+1/[(3*4)/2]+1/[(4*5)/2]+。+1/[(100*101)/2]=1+2/(1*2)+2/(2*3)+2/(3*4)+2/(4*5)+。+2/(100*101)=1+2[1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+。+1/(100*101)]=1+2*(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+。+1/100-1/101)=1+2*(1-1/101)=1+2*100/101=1+200/101=301/101