limit n tends to infinity = (n-1)(2n-1)/6n

arun how have you solved this and got answer

the above limit is infinity and hence does not exist. the reason is that numerator is quadratic and denominator is linear, so after performing polynomial division, you will have 2n+ L1/L2, where L1 and L2 are linear terms. since lim n tends to infinity (n-1)(2n-1)/6n= lim n tends to infinity 2n+lim L1/L2= infinity + some constant= infinity, hence the limit is +infinity which by definition is said to not exist. if u have firther doubts feel free to ask