$\genfrac{}{}{0ex}{}{3-1}{1.3}+\genfrac{}{}{0ex}{}{5-3}{3.5}+\genfrac{}{}{0ex}{}{7-5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101-99}{99.101}$

$=\genfrac{}{}{0ex}{}{3}{1.3}-\genfrac{}{}{0ex}{}{1}{1.3}+\genfrac{}{}{0ex}{}{5}{3.5}-\genfrac{}{}{0ex}{}{3}{3.5}+\genfrac{}{}{0ex}{}{7}{5.7}-\genfrac{}{}{0ex}{}{5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101}{99.101}-\genfrac{}{}{0ex}{}{99}{99.101}$ 

$=1-\genfrac{}{}{0ex}{}{1}{3}+\genfrac{}{}{0ex}{}{1}{3}-\genfrac{}{}{0ex}{}{1}{5}+\genfrac{}{}{0ex}{}{1}{5}-\genfrac{}{}{0ex}{}{1}{7}+\dots +\genfrac{}{}{0ex}{}{1}{99}-\genfrac{}{}{0ex}{}{1}{101}$

$=1-\genfrac{}{}{0ex}{}{1}{101}=\genfrac{}{}{0ex}{}{100}{101}$

Vậy $\genfrac{}{}{0ex}{}{2}{1.3}+\genfrac{}{}{0ex}{}{2}{3.5}+\genfrac{}{}{0ex}{}{2}{5.7}+\dots +\genfrac{}{}{0ex}{}{2}{99.101}=\genfrac{}{}{0ex}{}{100}{101}$.

$\genfrac{}{}{0ex}{}{3-1}{1.3}+\genfrac{}{}{0ex}{}{5-3}{3.5}+\genfrac{}{}{0ex}{}{7-5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101-99}{99.101}$

$=\genfrac{}{}{0ex}{}{3}{1.3}-\genfrac{}{}{0ex}{}{1}{1.3}+\genfrac{}{}{0ex}{}{5}{3.5}-\genfrac{}{}{0ex}{}{3}{3.5}+\genfrac{}{}{0ex}{}{7}{5.7}-\genfrac{}{}{0ex}{}{5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101}{99.101}-\genfrac{}{}{0ex}{}{99}{99.101}$ 

$=1-\genfrac{}{}{0ex}{}{1}{3}+\genfrac{}{}{0ex}{}{1}{3}-\genfrac{}{}{0ex}{}{1}{5}+\genfrac{}{}{0ex}{}{1}{5}-\genfrac{}{}{0ex}{}{1}{7}+\dots +\genfrac{}{}{0ex}{}{1}{99}-\genfrac{}{}{0ex}{}{1}{101}$

$=1-\genfrac{}{}{0ex}{}{1}{101}=\genfrac{}{}{0ex}{}{100}{101}$

Vậy $\genfrac{}{}{0ex}{}{2}{1.3}+\genfrac{}{}{0ex}{}{2}{3.5}+\genfrac{}{}{0ex}{}{2}{5.7}+\dots +\genfrac{}{}{0ex}{}{2}{99.101}=\genfrac{}{}{0ex}{}{100}{101}$.

$\genfrac{}{}{0ex}{}{3-1}{1.3}+\genfrac{}{}{0ex}{}{5-3}{3.5}+\genfrac{}{}{0ex}{}{7-5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101-99}{99.101}$

$=\genfrac{}{}{0ex}{}{3}{1.3}-\genfrac{}{}{0ex}{}{1}{1.3}+\genfrac{}{}{0ex}{}{5}{3.5}-\genfrac{}{}{0ex}{}{3}{3.5}+\genfrac{}{}{0ex}{}{7}{5.7}-\genfrac{}{}{0ex}{}{5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101}{99.101}-\genfrac{}{}{0ex}{}{99}{99.101}$ 

$=1-\genfrac{}{}{0ex}{}{1}{3}+\genfrac{}{}{0ex}{}{1}{3}-\genfrac{}{}{0ex}{}{1}{5}+\genfrac{}{}{0ex}{}{1}{5}-\genfrac{}{}{0ex}{}{1}{7}+\dots +\genfrac{}{}{0ex}{}{1}{99}-\genfrac{}{}{0ex}{}{1}{101}$

$=1-\genfrac{}{}{0ex}{}{1}{101}=\genfrac{}{}{0ex}{}{100}{101}$

Vậy $\genfrac{}{}{0ex}{}{2}{1.3}+\genfrac{}{}{0ex}{}{2}{3.5}+\genfrac{}{}{0ex}{}{2}{5.7}+\dots +\genfrac{}{}{0ex}{}{2}{99.101}=\genfrac{}{}{0ex}{}{100}{101}$.

$\genfrac{}{}{0ex}{}{3-1}{1.3}+\genfrac{}{}{0ex}{}{5-3}{3.5}+\genfrac{}{}{0ex}{}{7-5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101-99}{99.101}$

$=\genfrac{}{}{0ex}{}{3}{1.3}-\genfrac{}{}{0ex}{}{1}{1.3}+\genfrac{}{}{0ex}{}{5}{3.5}-\genfrac{}{}{0ex}{}{3}{3.5}+\genfrac{}{}{0ex}{}{7}{5.7}-\genfrac{}{}{0ex}{}{5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101}{99.101}-\genfrac{}{}{0ex}{}{99}{99.101}$ 

$=1-\genfrac{}{}{0ex}{}{1}{3}+\genfrac{}{}{0ex}{}{1}{3}-\genfrac{}{}{0ex}{}{1}{5}+\genfrac{}{}{0ex}{}{1}{5}-\genfrac{}{}{0ex}{}{1}{7}+\dots +\genfrac{}{}{0ex}{}{1}{99}-\genfrac{}{}{0ex}{}{1}{101}$

$=1-\genfrac{}{}{0ex}{}{1}{101}=\genfrac{}{}{0ex}{}{100}{101}$

Vậy $\genfrac{}{}{0ex}{}{2}{1.3}+\genfrac{}{}{0ex}{}{2}{3.5}+\genfrac{}{}{0ex}{}{2}{5.7}+\dots +\genfrac{}{}{0ex}{}{2}{99.101}=\genfrac{}{}{0ex}{}{100}{101}$.

$\genfrac{}{}{0ex}{}{3-1}{1.3}+\genfrac{}{}{0ex}{}{5-3}{3.5}+\genfrac{}{}{0ex}{}{7-5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101-99}{99.101}$

$=\genfrac{}{}{0ex}{}{3}{1.3}-\genfrac{}{}{0ex}{}{1}{1.3}+\genfrac{}{}{0ex}{}{5}{3.5}-\genfrac{}{}{0ex}{}{3}{3.5}+\genfrac{}{}{0ex}{}{7}{5.7}-\genfrac{}{}{0ex}{}{5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101}{99.101}-\genfrac{}{}{0ex}{}{99}{99.101}$ 

$=1-\genfrac{}{}{0ex}{}{1}{3}+\genfrac{}{}{0ex}{}{1}{3}-\genfrac{}{}{0ex}{}{1}{5}+\genfrac{}{}{0ex}{}{1}{5}-\genfrac{}{}{0ex}{}{1}{7}+\dots +\genfrac{}{}{0ex}{}{1}{99}-\genfrac{}{}{0ex}{}{1}{101}$

$=1-\genfrac{}{}{0ex}{}{1}{101}=\genfrac{}{}{0ex}{}{100}{101}$

Vậy $\genfrac{}{}{0ex}{}{2}{1.3}+\genfrac{}{}{0ex}{}{2}{3.5}+\genfrac{}{}{0ex}{}{2}{5.7}+\dots +\genfrac{}{}{0ex}{}{2}{99.101}=\genfrac{}{}{0ex}{}{100}{101}$.

$\genfrac{}{}{0ex}{}{3-1}{1.3}+\genfrac{}{}{0ex}{}{5-3}{3.5}+\genfrac{}{}{0ex}{}{7-5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101-99}{99.101}$

$=\genfrac{}{}{0ex}{}{3}{1.3}-\genfrac{}{}{0ex}{}{1}{1.3}+\genfrac{}{}{0ex}{}{5}{3.5}-\genfrac{}{}{0ex}{}{3}{3.5}+\genfrac{}{}{0ex}{}{7}{5.7}-\genfrac{}{}{0ex}{}{5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101}{99.101}-\genfrac{}{}{0ex}{}{99}{99.101}$ 

$=1-\genfrac{}{}{0ex}{}{1}{3}+\genfrac{}{}{0ex}{}{1}{3}-\genfrac{}{}{0ex}{}{1}{5}+\genfrac{}{}{0ex}{}{1}{5}-\genfrac{}{}{0ex}{}{1}{7}+\dots +\genfrac{}{}{0ex}{}{1}{99}-\genfrac{}{}{0ex}{}{1}{101}$

$=1-\genfrac{}{}{0ex}{}{1}{101}=\genfrac{}{}{0ex}{}{100}{101}$

Vậy $\genfrac{}{}{0ex}{}{2}{1.3}+\genfrac{}{}{0ex}{}{2}{3.5}+\genfrac{}{}{0ex}{}{2}{5.7}+\dots +\genfrac{}{}{0ex}{}{2}{99.101}=\genfrac{}{}{0ex}{}{100}{101}$.

$\genfrac{}{}{0ex}{}{3-1}{1.3}+\genfrac{}{}{0ex}{}{5-3}{3.5}+\genfrac{}{}{0ex}{}{7-5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101-99}{99.101}$

$=\genfrac{}{}{0ex}{}{3}{1.3}-\genfrac{}{}{0ex}{}{1}{1.3}+\genfrac{}{}{0ex}{}{5}{3.5}-\genfrac{}{}{0ex}{}{3}{3.5}+\genfrac{}{}{0ex}{}{7}{5.7}-\genfrac{}{}{0ex}{}{5}{5.7}+\dots +\genfrac{}{}{0ex}{}{101}{99.101}-\genfrac{}{}{0ex}{}{99}{99.101}$ 

$=1-\genfrac{}{}{0ex}{}{1}{3}+\genfrac{}{}{0ex}{}{1}{3}-\genfrac{}{}{0ex}{}{1}{5}+\genfrac{}{}{0ex}{}{1}{5}-\genfrac{}{}{0ex}{}{1}{7}+\dots +\genfrac{}{}{0ex}{}{1}{99}-\genfrac{}{}{0ex}{}{1}{101}$

$=1-\genfrac{}{}{0ex}{}{1}{101}=\genfrac{}{}{0ex}{}{100}{101}$

Vậy $\genfrac{}{}{0ex}{}{2}{1.3}+\genfrac{}{}{0ex}{}{2}{3.5}+\genfrac{}{}{0ex}{}{2}{5.7}+\dots +\genfrac{}{}{0ex}{}{2}{99.101}=\genfrac{}{}{0ex}{}{100}{101}$.