ab/(a+b-1)(a+b)+ab/(a+b)(a+b+1)+ab/(a+b+1)(a+b+2)+…+ab/(a+b+

原式=ab[1/(a+b-1)(a+b)+1/(a+b)(a+b+1)+1/(a+b+1)(a+b+2)+…+1/(a+b+98)(a+b+99)+1/(a+b+99)(a+b+100)]=ab[1/(a+b-1)-1/(a+b)+1/(a+b)-1/(a+b+1)+1/(a+b+1)-1/(a+b+2)+…+1/(a+b+98)-1/(a+b+99)+1/(a+b+99)-1/(a+b+100)]
=ab[1/(a+b)-1/(a+b+100)]=75/49