[latex] frac{3n+5}{n+1} [/latex]uzasadnij ,że ciąg an =jest ciagiem malejacym

[latex]a_n= frac{3n+5}{n+1}\ a_{n+1}=frac{3(n+1)+5}{n+1+1}=frac{3n+8}{n+2}\\\ a_{n+1}-a_n=frac{3n+8}{n+2}- frac{3n+5}{n+1}=frac{(3n+8)(n+1)}{(n+1)(n+2)}- frac{(3n+5)(n+2)}{(n+1)(n+2)}=\ = frac{3 n^2+11 n+8}{(n+1)(n+2)}- frac{3 n^2+11 n+10}{(n+1)(n+2)}= frac{3 n^2+11 n+8-3 n^2-11 n-10}{(n+1)(n+2)}= -frac{2}{(n+1)(n+2)} < 0[/latex]

[latex] frac{3n+5}{n+1} [/latex]uzasadnij ,że ciąg an =jest ciagiem malejacym

[latex] frac{3n+5}{n+1} [/latex]uzasadnij ,że ciąg an =jest ciagiem malejacym...