IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

nrki99

calculate :

lim (m/n)^x (1-{m/n})^n-x (n! / n-x! x! )

x~

vinu

Ans is 0.

ace

MR it would be very kind from your part if you edited that message if u meant it; i would like to tell you even we can understand such stuff .We all are a part of a community which respects each other
and i would also like to tell you that if you are not going to remove that the repercussions will be extreme at least from my side.

rahul_c

lim {1-(m/n)}^n = e^(-m)
n->i

i means infinity

lim n!/((n-x)!*x!) (m/n)^x*{1-(m/n)}^(n-x)
n->i

lim n!/((n-x)!*x!)* [(m/n)^x*{1-(m/n)}^n )/(1 - ( m/n))^x
n->i

usind

lim {1-(m/n)}^n = e^(-m)
n->i

when n->i { [n!/(n-x)!]/n^x} becomes 1

therefore we get {e^(-m)*m^x}/x!

rahul_c

Mr . rony kindly edit your post

vinu

Hi rahul_c,
it is x->i NOT n->i [where i means infinity];
I did like upto....
(1- m/n)^n lim {(n/m) -1}^-x * C(n,x) ;
[where C(n,x) means n C x];
Since C(n,x)=0 ,
the entire lim =0.

rahul_c

Thanks Vinu .i have realised my mistake

vinu

Thanks ADMIN............

I've edited my post too.

Suhail

mr roni plz dont try this again plz do not repeat it again

Admin

posts by rony and psr have been deleted.

rony, since this is done after repeated warning, unfortunately the account is being locked.

~admin

nrki99

no one anwers my question correctly

the correct ans is m^x e^m/x!

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