<transcript><audio_44>times a to the power n minus i b to the power of i all right that that's the general binomial formula by newton so i will use this formula for this and for this case and that will</transcript><transcript><audio_45>basically prove that every element of the sound on the left would be greater than the corresponding element of the sum on the right that's what i'm going to prove</transcript><transcript><audio_46>now one more interesting thing the number of elements in this sum in this case it's n in this case it's n minus one so um the number of elements is greater than here</transcript><transcript><audio_47>so from zero from one um from from zero to n and here from zero to n minus one so what i'm going to do is uh that if every member on the left is greater than corresponding member on the right</transcript><transcript><audio_48>plus in addition this member also has one extra member that would make it even better right all right so all i have to do is have i th member of this sum i will compare with ice member of that sum and i will show that</transcript><transcript><audio_49>one is greater than another all right for every i from 0 to n minus 1. now what's my ice member on the left well a is 1</transcript> times a to the power n minus i b to the power of i all right that that's the general binomial formula by newton so i will use this formula for this and for this case and that will basically prove that every element of the sound on the left would be greater than the corresponding element of the sum on the right that's what i'm going to prove now one more interesting thing the number of elements in this sum in this case it's n in this case it's n minus one so um the number of elements is greater than here so from zero from one um from from zero to n and here from zero to n minus one so what i'm going to do is uh that if every member on the left is greater than corresponding member on the right plus in addition this member also has one extra member that would make it even better right all right so all i have to do is have i th member of this sum i will compare with ice member of that sum and i will show that one is greater than another all right for every i from 0 to n minus 1. now what's my ice member on the left well a is 1
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