B=\(\frac{12}{2^2.4^2}+\frac{20}{4^2.6^2}+......+\frac{388}{96^2.98^2}+\frac{396}{98^2.100^2}\)
=\(\frac{1}{2^2}-\frac{1}{4^2}+\frac{1}{4^2}-\frac{1}{6^2}+...+\frac{1}{96^2}-\frac{1}{98^2}+\frac{1}{98^2}-\frac{1}{100^2}\)
=\(\frac{1}{2^2}-\frac{1}{100^2}\)
=\(\frac{2599}{10000}< \frac{2500}{10000}=\frac{1}{4}\)
=> B<\(\frac{1}{4}\)