Use the binomial theorem to show that (n 0) + (n 2) + (n 4) +.... = (n 1) + (n 3
ID: 3042619 • Letter: U
Question
Use the binomial theorem to show that (n 0) + (n 2) + (n 4) +.... = (n 1) + (n 3) + (n 5) +...
This picture below shows the process that i was going with the left hand side of the equation, but i am not rly getting anywhere because with the variables that i created, i am not able to get the results that I want. Can anyone help or show me where i went wrong?
https://scontent-ort2-1.xx.fbcdn.net/v/t1.0-9/27752359_10210833126359814_865532622814419151_n.jpg?oh=0c13eaf5953d918c1de53ef3c8d0e162&oe=5B091D6A
Explanation / Answer
It's quite simple really.
Binomial Theorem formula =
(a + b)n = nC0 an + nC1 a(n-1) b + nC2 a(n-2) b2 + ... + nCn bn
Letting a = -1 and b = 1, we get :
(0)n = nC0 - nC1 + nC2 - nC3 + nC4 - nC5 + nC6 ...
0 = nC0 - nC1 + nC2 - nC3 + nC4 - nC5 + nC6 ...
nC0 + nC2 + nC4 +... = nC1 + nC3 + nC5 +...
Hence Proved.
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