$$\lim \limits_{\ell \to\infty}\ \left[\ell-\dfrac{\ell}{e}\left(1+\dfrac{1}{\ell}\right)^\ell\right]\text{ oldugundan}$$
$$\lim \limits_{\ell \to\infty}\ \left[\ell-\dfrac{\ell}{e}\left(1+\dfrac{1}{\ell}\right)^\ell\right]$$$$=$$$$\left[\lim \limits_{\ell \to\infty}\ell-\left[\lim \limits_{\ell \to\infty}\dfrac{\ell}{e}\right].\underbrace{\lim \limits_{\ell \to\infty}\left(1+\dfrac{1}{\ell}\right)^\ell}_{e}\right]$$$$=$$$$\left[\lim \limits_{\ell \to\infty}\ell-\lim \limits_{\ell \to\infty}\ell.\underbrace{\dfrac{1}{e}.e}_1\right]$$
$$=$$$$\lim \limits_{\ell \to\infty}\ell-\lim \limits_{\ell \to\infty}\ell$$oluyor ,bildigim kadarıyla bu sonuc tanımsız, acaba ne yapmalıyız ki bir limit bulabılelım veya bulabılmemız mumkun mudur?