A = 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ........... + 1/99 - 1/100
A = 1/4 - 1/100
A = 6/25
=1/4-1/5+1/5-1/6+...+1/99-1/100
=1/4-1/100
=6/25
A = \(\frac{1}{4x5}\)+ \(\frac{1}{5x6}\)+ \(\frac{1}{6x7}\)+..........+ \(\frac{1}{99x100}\)
A = \(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{100}\)
A = \(\frac{1}{4}-\frac{1}{100}\)
A = \(\frac{6}{25}\)