Prove that lim n→∞ (1+1/n)^mn=e^m if m is an integer

 If m is an integer then prove that lim  n      (1+1/n)^mn=e^m.  We will show you how you can prove lim  n      (1+1/n)^mn=e^m when m is any integer.

Steps to prove that lim  n      (1+1/n)^mn=e^m


Step1: lim  (n )   (1+1/n)^mn=e^m

                    

Step2: Use this formula, 

lim  (n ) [(1+c/n)n= e^c]

                                                    

 

Step3:   lim  (n )   [(1+1/n)^n]^m

                 

 (1+1/n)^n=e

Thus,  lim n [(1+1/n)^n]^m= e^m

Hence, it is proved that [(1+1/n)^n]^m= e^m, when m is an integer.


See Alsolimit of (1+2/n)^n || step-by-step Explanation                                                          

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