<transcript><audio_50>so i don't need this and b is 1 over n so this is 1 over n to the power of i now that's my member on the left</transcript><transcript><audio_51>i member where i is 0 1 2 3 etc up to n on the on the right uh it's correspondingly n minus 1 factorial</transcript><transcript><audio_52>minus 1 factorial i factorial and 1 over n minus 1 factorial so i would like to prove that this is</transcript><transcript><audio_53>first of all i factorial present in here and here so if i will compare it i don't really need i will prove that this is greater than this both are</transcript><transcript><audio_54>containing this multiplier i factorial so it doesn't really change the relationship between them so how can i prove that this is greater than this let me open all these factorials in this particular case what is n factorial</transcript><transcript><audio_55>it's n times n minus 1 etc etc up to 1 and minus i factorial is starting from n minus 1 to 1. so if i will divide one by another let me just write it again what happens here this is</transcript> so i don't need this and b is 1 over n so this is 1 over n to the power of i now that's my member on the left i member where i is 0 1 2 3 etc up to n on the on the right uh it's correspondingly n minus 1 factorial minus 1 factorial i factorial and 1 over n minus 1 factorial so i would like to prove that this is first of all i factorial present in here and here so if i will compare it i don't really need i will prove that this is greater than this both are containing this multiplier i factorial so it doesn't really change the relationship between them so how can i prove that this is greater than this let me open all these factorials in this particular case what is n factorial it's n times n minus 1 etc etc up to 1 and minus i factorial is starting from n minus 1 to 1. so if i will divide one by another let me just write it again what happens here this is
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