ab/(a+b-1)(a+b)+ab/(a+b)(a+b+1)+ab/(a+b+1)(a+b+2)+.+ab/(a+b+98)(a+b+99)+ab/(a+b+99)(a+b+100)
=ab[1/(a+b-1)-1/(a+b)+1/(a+b)-1/(a+b+1)+.+1/(a+b+98)-1/(a+b+99)+1/(a+b+99)-1/(a+b+100)]
=ab*[1/(a+b-1)-1/(a+b+100)]
=ab(a+b+100-a-b+1)/[(a+b-1)(a+b+100)]
=101ab/[(a+b-1)(a+b+100)]