*A=($\dfrac{1}{1}$-$\dfrac{1}{2}$) + ($\dfrac{1}{3}$-$\dfrac{1}{4}$+...+$\dfrac{1}{101}$-$\dfrac{1}{102}$)
A =($\dfrac{1}{1}$-$\dfrac{1}{2}$+$\dfrac{1}{3}$-$\dfrac{1}{4}$+...+$\dfrac{1}{101}$-$\dfrac{1}{102}$)
A = ($\dfrac{1}{1}$+$\dfrac{1}{2}$+$\dfrac{1}{3}$+...+$\dfrac{1}{102}$) - 2($\dfrac{1}{2}$+$\dfrac{1}{4}$+...+$\dfrac{1}{102}$)
A=($\dfrac{1}{1}$+$\dfrac{1}{2}$+$\dfrac{1}{3}$+...+$\dfrac{1}{102}$)-($\dfrac{1}{1}$+$\dfrac{1}{2}$+$\dfrac{1}{51}$ )= $\dfrac{1}{52}$+$\dfrac{1}{53}$+...+$\dfrac{1}{101}$+$\dfrac{1}{102}$
A=($\dfrac{1}{52}$+$\dfrac{1}{102}$)+($\dfrac{1}{53}$+$\dfrac{1}{101}$)+...+($\dfrac{1}{76}$+$\dfrac{1}{78}$)+$\dfrac{1}{77}$
A=$\dfrac{154}{52.102}$+$\dfrac{154}{53.101}$+...+$\dfrac{154}{76.78}$+$\dfrac{154}{77.154}$
*B=($\dfrac{1}{52.102}$+$\dfrac{1}{102.52}$)+($\dfrac{1}{53.101}$+$\dfrac{1}{101.53}$)+...+($\dfrac{1}{76.78}$+$\dfrac{1}{78.76}$)+$\dfrac{2}{77.154}$
B=$\dfrac{2}{52.102}$+$\dfrac{2}{53.101}$+...+$\dfrac{2}{76.78}$+$\dfrac{2}{77.154}$
$\Longrightarrow$$\dfrac{A}{B}$=$\dfrac{154}{2}$=77
