\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
=\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
=\(\frac{1}{3}-\frac{1}{8}\)
=\(\frac{8}{24}-\frac{3}{24}\)
=\(\frac{5}{24}\)
= \(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{7}-\frac{1}{8}\)
= \(\frac{1}{3}-\frac{1}{8}\)
= \(\frac{5}{24}\)
=1/3-1/4+1/4-1/5+...+1/7-1/8
=1/3-1/8
=5/24