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ВинтЛили
@ВинтЛили
August 2022
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Найти предел. Срочно.
lim(n->∞)(((2^(n)+1)*(2n+1))/(2^(n+1)+1))
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nek0100
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))=∞
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ВинтЛили
Спасибо большое)
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Answers & Comments
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))=∞