Sabe-se que

$$\underset{n\to +\infty }{\lim }{a}_n=e\sqrt{2}$$ $$\underset{k\to +\infty }{\lim }{b}_k=2\sqrt{e}$$ $$\underset{h\to +\infty }{\lim }\sum _{j=1}^h{p}_j=+\infty$$ $p_j>0$, qualquer que seja $j=1,2,3,{}_{\cdots }$

Calcule: $$\underset{\ell \to +\infty }{\lim }\left(\frac{{\sum }_{i=1}^{\ell }{a}_i{b}_i}{\ell }+\frac{{\sum }_{i=1}^{\ell }{p}_i{b}_i}{{\sum }_{i=1}^{\ell }}\right)$$