Question Number 102545 by 175mohamed last updated on 09/Jul/20

Answered by mathmax by abdo last updated on 13/Jul/20

Σ_(n=1) ^∞  ((n^(1,2) −1)/(n^(2,3) +1)) =Σ_(n=1) ^∞  ((n^(6/5) −1)/(n^((23)/(10))  +1)) =Σ_(n=1) ^∞  U_n   U_n ∼ (n^(6/5) /n^((23)/(10)) ) =(1/n^(((23)/(10))−(6/5)) ) =(1/n^((23−12)/(10)) ) =(1/n^((11)/(10)) )  and Σ(1/n^((11)/(10)) ) is convergent (((11)/(10))>1) ⇒Σ U_n converges