Răspuns:
Explicație pas cu pas:
[tex]Ex7.~Dupa~Gauss,~a_{n}=\frac{n*(n+1)}{2},~~ a_{n+1}=\frac{(n+1)*(n+2)}{2},~deci~\frac{a_{n+1}}{a_{n}}= a_{n+1}:a_{n}=\frac{(n+1)*(n+2)}{2}:\frac{n*(n+1)}{2}=\frac{(n+1)*(n+2)}{2}*\frac{2}{n*(n+1)}=\frac{n+2}{n} \\Ex8.~0,9(7)=\frac{97-9}{90} =\frac{88}{90} =\frac{44}{45},~deci~\frac{n^{2}+n-2}{n(n+1)}=\frac{44}{45},~45n^{2}+45n-90=44n^{2}+44n,~n^{2}+n-90=0,~delta=361,~n=9.\\Raspuns:~0,9(7)~este~termenul~al~9-lea~in~sir.\\[/tex]
Ex9. x₁=1; x₂=4
x₃=2·x₂-x₁-2·2+5=2·4-1-4+5=8
x₄=2·x₃-x₂-2·3+5=2·8-4-6+5=11
x₅=2·x₄-x₃-2·4+5=2·11-8-8+5=27-16=11
x₆=2·x₅-x₄-2·5+5=2·11-11-10+5=27-21=6.
