a) [latex]a_n = |5 - n|\ a_{n + 1} - a_n = |5 - (n + 1)| - |5 - n| = |4 - n| - |5 - n|\ n < 4 Rightarrow a_{n + 1} - a_n = -1 < 0\ n > 5 Rightarrow a_{n + 1} - a_n = 1 > 0[/latex] b) [latex]a_n = frac{1}{n - 9,5}\ a_{n+1}-a_n=frac{1}{n + 1- 9,5}-frac{1}{n - 9,5}=frac{1}{n - 8,5}-frac{1}{n - 9,5}=frac{n - 9,5 - (n - 8,5)}{(n - 8,5)(n - 9,5)}=- frac{1}{(n - 8,5)(n - 9,5)} \ n = 9 Rightarrow a_{n+1}-a_n > 0 \ n = 10 Rightarrow a_{n+1}-a_n < 0[/latex] c) [latex]a_n = n^6-6n\ a_{n+1}-a_n=(n+1)^2-6(n+1)-n^2+6n = (n+1-n)(n+1+n)-6 = 2n-5\ n = 2 Rightarrow a_{n+1}-a_n < 0\ n = 3 Rightarrow a_{n+1}-a_n > 0[/latex] d) [latex]a_n = (-2)^{n - 1}\ a_{n+1}-a_n=(-2)^{n}-(-2)^{n - 1} = (-2)^{n - 1}(-2-1) = -3*(-2)^{n - 1}\ n = 3 Rightarrow a_{n+1}-a_n < 0\ n = 4 Rightarrow a_{n+1}-a_n > 0[/latex] jak masz pytania to pisz na pw
