Question

Se considera (an),definit prin a1=1 si an+1=an+1/an,n apartine N stelat.Sa se arate ca sirul (an) este strict crescator.

Answer 1

[tex]a_{n+1}-a_{n}= \frac{1}{a_n} \ \textgreater \ 0,\forall n \geq1=\ \textgreater \ \\ a_{n+1}\ \textgreater \ a_{n},\forall n \geq=\ \textgreater \ (a_n)~strict ~crescator[/tex]