Question

Am nevoie de ajutor urgent /: . Cum sa calculez limita sirurilor folosindu ma de criteriul raportului?

Answer 1

a)lim  an+1/an=lim e^(n+1)/n!:e^n/n!=[e*e^n/n!*(n+1)]*n!/e^n=[e*e^n/e^n]*n!/(n+1)*n!=e*1*1/(n+1)=0=>   an→0
b) lim   an+1/an=lim[(n+1)/a^(n+1)]:n/a^n=
lim [(n+1)/a*a^n]*a^n/n=
lim[(n+1)/n]*[a*a^n/a^n=1*a*1=a  daca   a>1   an→∞ 
daca  a<1  an→a
c)an=n!/2^n
lim  an+1/an=lim [ (n+1)!/2^(n+1)]:n!/2^n=
lim [(n!*(n+1)/2*2^n]*2^n/n1=lim[n!(n+1)/n!]*2^n/2*2^n=lim(n+1)/2]=∞=>
an→∞