a) \(\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{99\times100}\)
\(=\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
b) \(\frac{3}{1\times4}+\frac{3}{4\times7}+...+\frac{3}{91\times94}\)
\(=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-...+\frac{1}{91}-\frac{1}{94}\)
\(=\frac{1}{1}-\frac{1}{94}\)
\(=\frac{93}{94}\)
1/2x3 + 1/3x4 + ..... + 1/99x100
= 1/2 - 1/3 + 1/3 - 1/4 + ..... + 1/99 - 1/100
= 1/2 - 1/100
= 49/100
3/1x4 + 3/4x7 + .... + 3/91x94
= 3 - 3/4 + 3/4 - 3/7 + .....+ 3/91 - 3/94
= 3 - 3/94
= 279/94
a) \(\frac{1}{2.3}+\frac{1}{3.4}+......+\frac{1}{99.100}\)
\(=\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}.......-\frac{1}{99}+\frac{1}{99}+\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
b) \(\frac{3}{1.4}+\frac{3}{4.7}+......+\frac{3}{91.94}\)
\(=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-.......+\frac{1}{91}-\frac{1}{94}\)
\(=1-\frac{1}{94}\)
\(=\frac{93}{94}\)
a)\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}\)
\(=\frac{49}{100}\)
b)\(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{91.94}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{91}-\frac{1}{94}\)
\(=1-\frac{1}{94}\)
\(=\frac{93}{94}\)
