Question

\(\frac{15}{11.14}\)+\(\frac{15}{14.17}\)+\(\frac{15}{17.20}\)+...+\(\frac{15}{74.77}\)

Answer 1

\(\frac{15}{11.14}+\frac{15}{14.17}+\frac{15}{17.20}+.......+\frac{15}{74.77}\)

\(=5\left(\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}+.......+\frac{3}{74.77}\right)\)

\(=5\left(\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}+.....+\frac{1}{74}-\frac{1}{77}\right)\)

\(=5\left(\frac{1}{11}-\frac{1}{77}\right)\)

\(=5\left(\frac{7}{77}-\frac{1}{77}\right)\)

\(=5.\frac{6}{77}\)

\(=\frac{30}{77}\)