\(\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-....-\frac{1}{2.1}\)
=\(-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\right)\)
=\(-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\right)\)
=\(-\left(1-\frac{1}{100}\right)\)
=\(\frac{-99}{100}\)
A=1/100.99 - 1/99.98 - 1/98.97 -...- 1/3.2 - 1/2.1
A= - (1/100.99 + 1/99.98 + 1/98.97 +...+ 1/3.2 + 1/2.1)
A= - (1/2.1+1/3.2 +...+1/98.97+ 1/99.98 +1/100.99 )
A= - (1/1.2+1/2.3+1/3.4+...+1/97.98+ 1/98.99 +1/99.100)
A= - (1/1-1/2+1/2-1/3+1/3......-1/98+1/98-1/99+1/99-1/100)
A= - (1/1-1/100)
A= - 99/100
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