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.
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