B=\(\frac{6}{1.3}+\frac{6}{3.5}+\frac{6}{5.7}+......+\frac{6}{99.101}\)
=\(6.\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+.......+\frac{1}{99.101}\right)\)
=\(6\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+......+\frac{1}{99}-\frac{1}{101}\right)\)
=\(6.\left(1-\frac{1}{101}\right)\)
=\(6.\frac{100}{101}\)
=\(\frac{600}{101}\)