Question

1/2.5 + 1/5.8 + 1/8.11+...+1/296.299= ?

Answer 1

\(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{296.299}\)

=\(\frac{1}{3}\left(\frac{3}{2.5}+\frac{3}{5.7}+\frac{3}{7.11}+...+\frac{3}{296.299}\right)\)

=\(\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{296}-\frac{1}{299}\right)\)

=\(\frac{1}{3}\left(\frac{1}{2}-\frac{1}{299}\right)\)

=\(\frac{1}{3}.\frac{297}{598}\)

=\(\frac{99}{598}\)