N=\(3.\left(\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{197.199}\right)\)
N=\(\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{197.199}\right)\)
N=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{197}-\frac{1}{199}\right)\)
N=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{999}\right)\)
N=\(\frac{3}{2}.\frac{194}{995}\)
N=\(\frac{291}{995}\)
= 3/5-3/7+3/7-3/9+3/9-3/11+......+3/197-3/199
= 3/5-3/199
= 582/995