Question

Хелп, все на картинке!(вторая часть)))

Answer 1

$4)\; \; (1-y)dx-(2+x)dy=0\; ,\; \; (1-y)dx=(2+x)dy\\\\\int \frac{dx}{2+x}=\int \frac{dy}{1-y}\\\\ln|2+x|=-ln|1-y|+lnC\\\\2+x=\frac{C}{1-y}\\\\1-y=\frac{C}{2+x}\; ,\; \; y=1-\frac{C}{2+x}\\\\5)\; \; n=6!=1\cdot 2 \cdot 3\cdot 4\cdot 5\cdot 6=720\\\\6)\; \; \sum \limits _{n=1}^{\infty } \frac{3n^3-2}{n^2(5-n)}=\sum \limits _{n=1}^{\infty } \frac{3n^3-2}{-n^3+5n^2}\\\\\lim\limits _{n \to \infty} a_n=\lim\limits _{n \to \infty} \frac{3n^3-2}{-n^3+5n^2}=\lim\limits _{n \to \infty}\frac{3-\frac{2}{n^3}}{-1+\frac{5}{n}}=\\\\=\frac{3-0}{-1+0}=-3\ne 0\; \; \to \; \; \; rasxoditsya$