lim√[(3n^2)+1]/(7n+1)=?

lim√[(3n^2)+1]/(7n+1)=?

Lim √ (3N & # 178; + 1) / (7n + 1) as X - > ∞ = Lim [√ (3N & # 178; + 1) / N] / [(7n + 1) / N], divided by n = Lim √ [(3N & # 178; + 1) / N & # 178;] / [(7n + 1) / N] = Lim √ (3 + 1 / N & # 178;) / [(7 + 1 / N) = √ (3 + 0) / (7 + 0) = √ 3 / 7

Lim [1 / (1 * 4) + 1 / (4 * 7) + 1 / (3n-1) (3N + 1)] how do I think the title is wrong,

Split term method
=lim 1/3 * (1 - 1/4 + 1/4 - 1/7 + ...+ 1/(3n-1) - 1/(3n+1 ) )
=lim 1/3 * (1 - 1/(3n+1) )
=lim n/(3n+1)
=1/3

Lim n * (- 1) ^ n (n 〉 positive infinity). If the value of this function fluctuates between positive infinity and negative infinity, is the limit of this function infinite?
Lim n * (- 1) ^ n (n 〉 positive infinity). The value of this function fluctuates between positive infinity and negative infinity. According to the definition | n * (- 1) ^ n | = n > m, is the limit of this function infinite? Is it written as infinity [the one without sign], or is there no infinity in this case?

It doesn't exist because + ∞≠ - ∞
The limit is infinite and does not exist, either + ∞ or - ∞