`=1/10-1/11+1/11-1/12+...+1/99-1/100`
`=1/10-1/100`
`=9/100`
\(\dfrac{1}{10.11}+\dfrac{1}{11.12}+...+\dfrac{1}{99.100}\\ =\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+..++\dfrac{1}{99}-\dfrac{1}{100}\\ =\dfrac{1}{10}-\dfrac{1}{100}\\ =\dfrac{10}{100}-\dfrac{1}{100}\\ =\dfrac{9}{100}\)
= 1/10-1/11+1/11-1/12+...+1/99-1/100
=1/10-1/100
=10/100-1/100
=9/100
=1/10-1/11+1/11-1/12+1/12-1/13+....+1/99-1/100
=1/10-1/100
=10/100-1/100
=9/100
`1/[10.11]+1/[11.12]+1/[12.13]+...+1/[99.100]`
`=1/10-1/11+1/11-1/12+1/12-1/13+....+1/99-1/100`
`=1/10-1/100`
`=10/100-1/100`
`=9/100`
\(\dfrac{1}{10.11}+\dfrac{1}{11.12}+\dfrac{1}{12.13}+...+\dfrac{1}{99.100}\)
\(=\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+...+\dfrac{1}{99}+\dfrac{1}{100}\)
\(=\dfrac{1}{10}-\dfrac{1}{100}\)
\(=\dfrac{9}{100}\)
