Question

\(\frac{9}{1.2}\) + \(\frac{9}{2.3}\) +\(\frac{9}{3.4}\) +...........+\(\frac{9}{98.99}\) +\(\frac{9}{99.100}\)

Answer 1

\(\frac{9}{1.2}+\frac{9}{2.3}+....+\frac{9}{98.99}+\frac{9}{99.100}\)

\(=9.\frac{1}{1.2}+9.\frac{1}{2.3}+....+9.\frac{1}{98.99}+9.\frac{1}{99.100}\)

\(=9.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)

\(=9.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)

\(=9.\left(1-\frac{1}{100}\right)=9.\frac{99}{100}=\frac{891}{100}\)