S = $\frac{1}{2.5}$ +....+ $\frac{1}{97.100}$
3S = $\frac{3}{2.5}$ +....+ $\frac{3}{97.100}$
3S = $\frac{1}{2}$ - $\frac{1}{5}$ + $\frac{1}{5}$ - $\frac{1}{8}$ +....+ $\frac{1}{97}$ - $\frac{1}{100}$
3S = $\frac{1}{2}$ - $\frac{1}{100}$
3S = $\frac{49}{100}$
S = $\frac{49}{100}$ : 3
S = $\frac{49}{300}$