[tex]1)\\\\a_{n} = \frac{2n+4}{n} = \frac{2(n+2)}{n}\\\\a_{n+1} = \frac{2(n+1+2)}{n+1} = \frac{2(n+3)}{n+1}\\\\r = a_{n+1}-a_{n}\\\\r = \frac{2(n+3)}{n+1}-\frac{2(n+2)}{n} = \frac{2n(n+3)-2(n+2)(n+1)}{n(n+1)} = \frac{2n^{2}+6n-2(n^{2}+n+2n+2)}{n(n+1)}=\\\\=\frac{2n^{2}+6n-2(n^{2}+3n+2)}{n(n+1)} = \frac{2n^{2}+6n-2n^{2}-6n-4}{n^{2}+n} = -\frac{4}{n^{2}+n} < 0[/tex]
r < 0, to ciąg jest malejący
[tex]2)\\\\a_{n} = -3n+7\\\\a_{n+1} = -3(n+1)+7 = -3n-3+7 = -3n+4\\\\r = a_{n+1}-a_{n} = -3n+4 - (-3n+7) = -3n+4+3n-7 = -3 < 0[/tex]
r < 0, to ciąg jest malejący
