\(F=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+......+\frac{3}{870}\)
\(=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+.....+\frac{3}{29.30}\)
\(=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{29}-\frac{1}{30}\right)\)
\(=3.\left(1-\frac{1}{30}\right)\)
\(=3.\frac{29}{30}\)
\(=\frac{29}{10}\)