value of integration , Mathematics

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 

Posted Date: 3/23/2013 12:36:38 AM | Location : United States







Related Discussions:- value of integration , Assignment Help, Ask Question on value of integration , Get Answer, Expert's Help, value of integration Discussions

Write discussion on value of integration
Your posts are moderated
Related Questions
a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k


State DeMorgan's law. Prove it using the truth table.   Ans: DeMorgan's law defines that    (i)  (x ∨ y)' = x' ∧ y' (ii)  (x ∧ y)' = x' ∨ y'      Now let us dr

A golf ball has a diameter equal to 4.1cm. Its surface has 150 dimples each of radius 2mm. Calculate the total surface area which is exposed to the surroundings assuming that the d

Write the subsequent 2nd order differential equation as a system of first order, linear differential equations. 2 y′′ - 5 y′ + y = 0  y (3) = 6  y′ (3) = -1  We can wri

i have to find surface,lateral,and volume

Find the values of x and y


ABCD is a rhombus. the sides of the rhombus are 8cm long .one of its diagonals is 12cm .find the angels of the rhombus

Two circles touch internally at a point P and from a point T on the common tangent at P, tangent segments TQ and TR are drawn to the two circles. Prove that TQ = TR. Given: