vb   

$A=\genfrac{}{}{0ex}{}{1}{6}+\genfrac{}{}{0ex}{}{1}{24}+\genfrac{}{}{0ex}{}{1}{60}+...+\genfrac{}{}{0ex}{}{1}{970200}$
$A=\genfrac{}{}{0ex}{}{1}{\mathrm{1.2.3}}+\genfrac{}{}{0ex}{}{1}{\mathrm{2.3.4}}+\genfrac{}{}{0ex}{}{1}{\mathrm{3.4.5}}+...+\genfrac{}{}{0ex}{}{1}{\mathrm{98.99.100}}$
Ta có:
$\genfrac{}{}{0ex}{}{1}{\mathrm{1.2.3}}=\genfrac{}{}{0ex}{}{1}{2}\left(\genfrac{}{}{0ex}{}{1}{1.2}-\genfrac{}{}{0ex}{}{1}{2.3}\right)$;
$\genfrac{}{}{0ex}{}{1}{\mathrm{2.3.4}}=\genfrac{}{}{0ex}{}{1}{2}\left(\genfrac{}{}{0ex}{}{1}{2.3}-\genfrac{}{}{0ex}{}{1}{3.4}\right)$;
...;
$\genfrac{}{}{0ex}{}{1}{\mathrm{98.99.100}}=\genfrac{}{}{0ex}{}{1}{2}\left(\genfrac{}{}{0ex}{}{1}{98.99}-\genfrac{}{}{0ex}{}{1}{99.100}\right)$
$A=\genfrac{}{}{0ex}{}{1}{2}\left(\genfrac{}{}{0ex}{}{1}{1.2}-\genfrac{}{}{0ex}{}{1}{2.3}+\genfrac{}{}{0ex}{}{1}{2.3}-\genfrac{}{}{0ex}{}{1}{3.4}+...+\genfrac{}{}{0ex}{}{1}{98.99}-\genfrac{}{}{0ex}{}{1}{99.100}\right)$
$A=\genfrac{}{}{0ex}{}{1}{2}\left(\genfrac{}{}{0ex}{}{1}{1.2}-\genfrac{}{}{0ex}{}{1}{99.100}\right)$
$A=\genfrac{}{}{0ex}{}{1}{2}\left(\genfrac{}{}{0ex}{}{99.100-2}{200.99}\right)$
$A=\genfrac{}{}{0ex}{}{1}{2}\left(\genfrac{}{}{0ex}{}{98998}{200.99}\right)=\genfrac{}{}{0ex}{}{49499}{19800}$

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