Răspuns:
Explicație pas cu pas:
7a) An+1 -An = (3n+3-1)/(5n+5+2) -(3n-1)/(5n+2) =
(3n+2)/(5n+7) -(3n-1)/(5n+2) =
(15n^2+6n+10n+4-15n^2+5n-21n+7 )/(5n+7)(5n+2)
=( 4+7 )/(5n+7)(5n+2) > 0,
deci An+1 -An > 0, An+1 > An sir crescator
8a) An+1 -An = (n+2)/(2n+3) - (n+1)/(2n+1) =
(2n^2+n +4n +2-2n^2-2n-3n-3)/(2n+3)(2n+1 ) =
(2-3)/(2n+3)(2n+1 ) < 0,
deci An+1 -An < 0, An+1 < An, sir decrescator
