\(\lim\limits_{n\to\infty}(1+\frac1n)^{pn+q}\)** (1**^{\(\infty\)} type)

= Exp{\(\lim\limits_{n\to\infty}(1+\frac1n-1)^{pn+q}\)}

= Exp {\(\lim\limits_{n\to\infty}\frac{pn+q}n\)}

= Exp{\(\lim\limits_{n\to\infty}(p+\frac qn)\)}

= Exp {P}

= Exp^{P}

∴ \(\lim\limits_{n\to\infty}(1+\frac 1n)^{pn+q}\) = e^{P}