\(\frac{1}{99.97}-\frac{1}{97.95}-...-\frac{1}{5.3}-\frac{1}{3.1}\)
\(=\frac{1}{97.99}-\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{95.97}\right)\)
\(=\frac{1}{97.99}-\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{95.97}\right)\)
\(=\frac{1}{97.99}-\frac{1}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{95}-\frac{1}{97}\right)\)
\(=\frac{1}{9603}-\frac{1}{2}\left(1-\frac{1}{97}\right)\)
\(=\frac{1}{9603}-\frac{1}{2}.\frac{96}{97}\)
\(=\frac{-4751}{9603}\)
A=-(1/99.97+1/97.95+...+1/5.3+1/3.1)
2B=2/99.97+2/97.95+...+2/5.3+2/3.1
2B=1-1/3+1/3-1/5+...+1/97-1/99
2B=1-1/99
2B=98/99
B=49/99
Suy ra A=-1/49/49
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