11nn Means n.n.n.n.n.n.n ntimes / n(n-1)(n-2)! Therefore it will be a Diverging series
I too think wat nishant bhaiyya interceptted is correct
The nth therm of a sequence in given by nn/n! ....
Show that this sequence converges and find it's limit...
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6 Answers
11
62the answer will be zero..
there are two ways to look at it..
n! < {(n+1)/2}n by AM GM inequality
thus,
n!/n^n < {(n+1)/2n2}n
and when n is large, (n+1)/2n2 tends to zero...
another way could be by saying that
1/n, 2/n..... (n/2)/n will be all less than 1/2
thus teh product will be less tahn
(1/2)n/2
since n tends to infinity.. this tends to zero :)
11bhaiyya , can u plese show the two terms whose am ur finding for AM GM Inequality.....please