\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{4.5.6}+....+\frac{1}{98.99.100}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{100}\)
\(=\frac{1}{1}-\frac{1}{100}\)
\(=\frac{99}{100}\)
2A=\(\frac{2}{1.2.3}\)+\(\frac{2}{2.3.4}\)+\(\frac{2}{4.5.6}\)+...+\(\frac{2}{98.99.100}\)
2A=\(\frac{1}{1.2}\)-\(\frac{1}{2.3}\)+\(\frac{1}{2.3}\)-\(\frac{1}{3.4}\)+..+\(\frac{1}{98.99}\)-\(\frac{1}{99.100}\)
2A=\(\frac{1}{1.2}\)-\(\frac{1}{99.100}\)=\(\frac{1}{2}\)-\(\frac{1}{9900}\)=\(\frac{4949}{9900}\)
A=\(\frac{4949}{9900}\):2
A=\(\frac{4949}{19800}\)
