We have:\(1-\dfrac{1}{1+2+......+n}=1-\dfrac{1}{\dfrac{n\left(n+1\right)}{2}}=1-\dfrac{2}{n\left(n+1\right)}=\dfrac{n\left(n+1\right)-2}{n\left(n+1\right)}=\dfrac{n^2+n-2}{n\left(n+1\right)}\)

\(=\dfrac{n^2-n+2n-2}{n\left(n+1\right)}=\dfrac{n\left(n-1\right)+2\left(n-1\right)}{n\left(n+1\right)}=\dfrac{\left(n+2\right)\left(n-1\right)}{n\left(n+1\right)}\)

Instead in the expression we have:

A=\(\dfrac{4.1}{2.3}+\dfrac{5.2}{3.4}+.......+\dfrac{1988.1985}{1986.1987}\)

\(=\dfrac{1.2....1985}{3.4....1987}.\dfrac{4.5.....1988}{2.3.....1986}\)

\(=\dfrac{1.2}{1986.1987}.\dfrac{1987.1988}{2.3}=\dfrac{1988}{3.1986}=\dfrac{1988}{5958}=\dfrac{994}{2979}\)

P/s:A is the expression