Prove that the sequence \( \left\langle\mathrm{S}_{n}\right\rangle \) where: \[ s_{n}=\frac{1}{1!}+\frac{1}{2!}+\ldots \ldots+\frac{1}{n!} \] is convergent.

4) Show that \( \lim _{z \rightarrow} \) \( i z^{3}+i z-1 \) \( 2 z+3 i(z-i) \)

\( \frac{d}{d x}\left(x^{3}+20 x+21\right) \) is (i) \( 3 x^{3}+20 \) (ii) \( 3 x^{2} \) (iii) 0 (iv) None of These

Answer any THREE. \( \lim _{x \rightarrow 1}\left(\frac{1}{x-1}-\frac{1}{\ln x}\right) \)

(Q6; 2,6 балла) Найдите наименьшее значение выражения \( 16 x+\frac{9}{25 x}(x>0) \), используя \( \frac{a+b}{2} \geq \sqrt{a b} \).

(4) show that \( \lim _{z \rightarrow a} \) \( \frac{i z^{3}+i z-1}{2 z+3 i(z-i)} \)