Can we compare them III?

Algebra Level 5

\[\begin{eqnarray} A&=&1+\dfrac{1}{4}+\dfrac{1\cdot 4}{4\cdot 8}+\dfrac{1\cdot 4 \cdot 7}{4 \cdot 8 \cdot 12}+ \dfrac{1 \cdot 4 \cdot 7 \cdot 10}{4 \cdot 8 \cdot 12 \cdot 16}+\ldots \\ B&=&1+\dfrac{2}{6}+\dfrac{2 \cdot 5}{6 \cdot 12}+\dfrac{2 \cdot 5 \cdot 8}{6 \cdot 12 \cdot 18}+\dfrac{2 \cdot 5 \cdot 8 \cdot 11}{6 \cdot 12 \cdot 18 \cdot 24}+\ldots \end{eqnarray} \]

Find the relationship between \(A\) and \(B\).

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