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
Proof of Constant Times a Function: (cf(x))′ = cf ′(x) It is very easy property to prove using the definition given you a recall, we can factor a constant out of a limit. No


Example : Back into the complex root section we complete the claim that y 1 (t ) = e l t cos(µt)        and      y 2 (t) = e l t sin(µt) Those were a basic set of soluti

Explain with the help of number line (-6)+(+5)

a triangle is 180

the number is 605176 the underline digit is 0

Application of rate change Brief set of examples concentrating on the rate of change application of derivatives is given in this section.  Example    Find out all the point

which one of the following examples represents a repeating decimal? 0.123123,1.111114,0.777777,4.252525?

What is Angle Pairs? Two angles are adjacent angles if they have the same vertex and share one side. Vertical angles are a pair of nonadjacent angles formed by two intersecting

Give some children around you a task in mathematics. The task should be in an area in which they' have not been given a large dose of algorithms and strategies. Do all of them foll