Ta có:

\(1.2.3....99=\dfrac{1.2.3.4....99.100}{2.4.6....100}\)

\(=\dfrac{1}{2.1}.\dfrac{2}{2.2}...\dfrac{100}{2.50}\)

\(=\dfrac{1.2.3.4....100}{1.2.3....50.2.2.2...2}\) ( \(50\) thừa số \(2\) )

\(=\dfrac{51.51...100}{2.2.2...2}\)

\(=\dfrac{51}{2}.\dfrac{52}{2}.\dfrac{53}{2}...\dfrac{100}{2}\)

\(\Rightarrow A=B\left(đpcm\right)\)

\(P=xy^2+x^2y^4+x^3y^6+...+x^{10}y^{20}\)