Question

Найти предел. Срочно.

lim(n->∞)(((2^(n)+1)*(2n+1))/(2^(n+1)+1))

Answer 1

lim(n->∞)(((2^(n)+1)*(2n+1))/(2^(n+1)+1))=
lim(n->∞)((2^(n)+1+2n+2^(n)*2*n)/(2^(n+1)+1))=
lim(n->∞)[(2^(n)/(2^(n+1)+1)+1/(2^(n+1)+1)+2n/(2^(n+1)+1)+2^(n)*2*n)/(2^(n+1)+1)]=...

lim(n->∞)(2^(n)/(2^(n+1)+1))=0
lim(n->∞)(1/(2^(n+1)+1))=0
lim(n->∞)(2n/(2^(n+1)+1))=0

...=lim(n->∞)(2^(n)*2*n)/(2^(n+1)+1))=lim(n->∞)(2^(n+1)*n)/(2^(n+1)+1))=∞

Answer 2

Спасибо большое)