Răspuns
g)Adui si scazi 1 la baza si aplici formula
lim(1+1/u(n))^u(n)=e
lim[1-1+(2n+√n+3)/(2n+1)]^√n=
[1+(2n+√n+3-2n-1)/(2n+1)]^√n=
[1+(√n+2)/(2n+1)]^√n
u(n)=(√n+2)/(2n+1)
Ridici baza simultan la puterea
(2n+1)/(√n+2)*(n+2)/(2n+1)=1
lim[[1+(√n+2)/(2n+1)]^(2n+1)/(√n+2)]]^(√n+2)/(2n+1)*√n=
e^lim(√n+2)/(2n+1)*√n=e^lim(n+2√n)/(2n+1)=e^1/2=√e
La fel procedezi si la h) adui si scazi 1 si-l aduci la forma
(1+1/u(n))^un
Explicație pas cu pas:
