Question

6/1(1+1) + 6/2(2+1)+ 6/3(3+1)+.......+ 6/ 100(100+1)=?

Answer 1

6/1(1+1) + 6/2(2+1)+ 6/3(3+1)+.......+ 6/ 100(100+1)

=6/(1•2)+6/(2•3)+6/(3x4)+...+6/(100•101)

=6[1/(1•2)+1/(2•3)+1/(3•4)+...+1/(100•101)]

=6[(1/1 -1/2)+(1/2-1/3)+(1/3-1/4)+….+(1/100-1/101)]

=6(1/1 - 1/101)

=6•(101-1)/101

=600/101