at 4:04 you evaluated the sum wrong. The sum from k+3 to N of 1 isnt just 1. there is a missing factor of (N-k-2). the limit still goes to zero so it doesnt affect the answer though.
@@cipherunityyes the sums cancel. But you are left with the negative sum from k+3 to N of (N-k+1)!/N!. But this is all independent of the index variable n so you are left with this term multiplied by the sum from k+3 to N of 1. The mistake that you have made is assuming this summation is equal to 1 when in-fact it is equal to (N-k-2)
@@43ash30 first term was taken out from the summation on left side and the last term was taken out from the summation on the left side. The index were fixed accodingly. The rest is simple math.
nice
at 4:04 you evaluated the sum wrong. The sum from k+3 to N of 1 isnt just 1. there is a missing factor of (N-k-2). the limit still goes to zero so it doesnt affect the answer though.
At 4:04 I do not see any mistake. We have just changed the index. The two two summations are identical and cancel each other.
@@cipherunityyes the sums cancel. But you are left with the negative sum from k+3 to N of (N-k+1)!/N!. But this is all independent of the index variable n so you are left with this term multiplied by the sum from k+3 to N of 1. The mistake that you have made is assuming this summation is equal to 1 when in-fact it is equal to (N-k-2)
@@43ash30 first term was taken out from the summation on left side and the last term was taken out from the summation on the left side. The index were fixed accodingly. The rest is simple math.
Did not understanf first step
I shall try to do videos on summation. Hopefully that shall help.