A=$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+….+\frac{1}{99.100}

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1. A=$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+….+\frac{1}{99.100}$

   A$=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+…+\frac{1}{99}-\frac{1}{100}$

   A$=1-\frac{1}{100}$

   A$=\frac{99}{100}$

   $\nocopy$

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2. A=$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+….+\frac{1}{99.100}$

   ⇔`(2-1)/1.2+(3-2)/2.3+(4-3)/3.44+…+(100-99)/99.100`

   ⇔`2/1.2-1/1.2+3/2.3-2/2.3+4/3.4-3/3.4+…+100/99.100-99/99.100`

   ⇔`1-1/2+1/2-1/3+1/3-1/4+…+1/99-1/100`

   ⇔`1-1/100`

   ⇔`99/100`

    

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