<transcript><audio_27>most important goal of my today's lecture to prove that this</transcript><transcript><audio_28>as n goes to infinity and this limit since i know it exists i called it e now i definitely know that this limit is in between two and three because in the previous lecture i actually proved that</transcript><transcript><audio_29>this expression for any n is in between two and three it's greater than two and less than e then less than three so there is some number in between two and three some real number um which i can call basically the letter e</transcript> most important goal of my today's lecture to prove that this as n goes to infinity and this limit since i know it exists i called it e now i definitely know that this limit is in between two and three because in the previous lecture i actually proved that this expression for any n is in between two and three it's greater than two and less than e then less than three so there is some number in between two and three some real number um which i can call basically the letter e
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