10 Giúp mình với!

Hurricane

a)

$u_{n+1}-u_n=\frac{n+1-3}{n+1+2}-\frac{n-3}{n+2}$

$=\frac{n-2}{n+3}-\frac{n-3}{n+2}$

$=\frac{n^2-4-n^2+9}{\left(n+3\right)\left(n+2\right)}$

$=\frac{5}{\left(n+3\right)\left(n+2\right)}>0\forall n\in\mathbb{N*}$

$\Rightarrow$ Dãy số tăng

b)

$u_{n+1}-u_n=\frac{3^{n+1}}{2^{n+1}.\left(n+1\right)!}-\frac{3^n}{2^n.n!}$

$=\frac{3^{n+1}}{2.2^n.n!.\left(n+1\right)}-\frac{3^n}{2^n.n!}$

$=\frac{3^{n+1}}{2^{n+1}.\left(n+1\right)!}-\frac{3^n.2\left(n+1\right)}{2^{n+1}.\left(n+1\right)!}$

$=\frac{3^n.\left(3-2n-2\right)}{2^{n+1}.\left(n+1\right)!}$

$=\frac{3^n.\left(-2n+1\right)}{2^{n+1}.\left(n+1\right)!}<0\forall n\in\mathbb{N*}$

$\Rightarrow$ Dãy số giảm

c)

$u_{n+1}-u_n=\left(-1\right)^{n+1}.\left(2^{n+1}+1\right)-\left(-1\right)^n.\left(2^n+1\right)$

$=\left(-1\right)^n.\left\lbrack\left(-1\right).\left(2^{n+1}+1\right)-2^n-1\right\rbrack$

$=\left(-1\right)^n.\left(-2^{n+1}-1-2^n-1\right)$

$=\left(-1\right)^n.\left(-3.2^n-2\right)$

$\Rightarrow$ Dãy số không tăng, không giảm.