Determine lg(1/2) + lg(2/3) + lg(3/4) + ... + lg(99/100)

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lg(1/2)+lg(2/3)+...+lg(99/100)

We know that:

logx1+lgx2+...lg(xn)=lg(x1*x2*...*xn)

==> lg(1/2)+lg(2/3)+...+lg(99/100)=lg(1/2*2/3*...*99/100)

  = lg(1/100) = lg(100)^-1

                  = -log(100)

                    =-lg(10)^2

                    =-2lg(10)=-2

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