convergence of the sequence (1+1/n)^n
The proof will be given by demonstrating that the sequence (1) is:
monotonic (increasing), that is
bounded above, that is for some
In order to prove part 1, consider the binomial expansion for :
Since , and since the sum has one term more than , it is demonstrated that the sequence (1) is monotonic.
In order to prove part 2, consider again the binomial expansion:
Since and :
which is the definition of the Napier’s constant.
|Title||convergence of the sequence (1+1/n)^n|
|Date of creation||2013-03-22 17:43:26|
|Last modified on||2013-03-22 17:43:26|
|Last modified by||kfgauss70 (18761)|