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
Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans:    S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot


which quadrilaterals have only 1 pair of parallel sides

application of derivatives in engg.

how to round off numbers to the nearest tens and to the nearest hundred

Computation of Covariance Ungrouped Data          For a population consisting of paired ungrouped data points {X, Y} where,

How can I use the I=Prt formula to get the interest for this problem? A car dealer sells me a car for $16450 with $3,290 down and $339.97 monthly payments for 48 months. What is

On a piece of machinery, the centers of two pulleys are 3 feet apart, and the radius of each pulley is 6 inches. Determine the size of belt (in feet) is required to wrap around bot


help to solve the laws of indicies chapter 9c book 3 high school example19to the power3_2 what is answer