<transcript><audio_20>as my n goes to infinity that means that my tangential line would be at angle 45 degrees so basically i have determined um that there is some kind of a number which is</transcript><transcript><audio_21>if used as e then this would be tending to 1. that's how that's how i define basically</transcript><transcript><audio_22>as a base of an exponential function which has this type of a tendency right okay now um i um kind of</transcript><transcript><audio_23>presume that this particular approximation exists and the approximation is um is is better and better as n increasing to infinity from which i have derived that</transcript><transcript><audio_24>e to the one and n approximately equals to 1 n plus 1 right so 1 plus 1 n over n and then i raise both sides into n's degrees so</transcript><transcript><audio_25>e is approximately 1 plus 1 n to the n now these manipulations with approximation is not exactly rigorous mathematically so today i'm um i'm going to prove the following thing</transcript><transcript><audio_26>that this sequence does have a limit um and then you can actually say that this limit is is this number all right so this is the</transcript> as my n goes to infinity that means that my tangential line would be at angle 45 degrees so basically i have determined um that there is some kind of a number which is if used as e then this would be tending to 1. that's how that's how i define basically as a base of an exponential function which has this type of a tendency right okay now um i um kind of presume that this particular approximation exists and the approximation is um is is better and better as n increasing to infinity from which i have derived that e to the one and n approximately equals to 1 n plus 1 right so 1 plus 1 n over n and then i raise both sides into n's degrees so e is approximately 1 plus 1 n to the n now these manipulations with approximation is not exactly rigorous mathematically so today i'm um i'm going to prove the following thing that this sequence does have a limit um and then you can actually say that this limit is is this number all right so this is the
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