Marginire siruri

[rucarr]

Să se studieze marginirea sirurilor
a) (1+3^n)/(1+2^n)
b) x1=1 , xn+1=(1/n)*xn , n>=1
c) x1=sqrt(2), xn+1=(n/(n+1))*xn, n>=1

[DD]

Xn=(1+3^n)/(1+2^n)=>x1=4/3 , lim(n->inf.)Xn=(3/2)^n.(1+1/3^n)/(1+1/2^n)->inf.
Xn=1/(n-1)!->x1=1,lim(n->inf)Xn=>0
Xn=√(2/)n=>x1=√(2,) lim(n=>inf)Xn=>0