Binomial (1 Viewer)

[dolbinau]

Binomial, specifically the ones that pop up in question 7 are impossible.

I get when they are like prove (x+1)^2 = (they have differentiated then sub x=1)

But how can I apply it to harder ones; is there a general rule I can look out for if I need to examine the relationships between coefficients (I think that's what a lot of them do, like find the terms of X^2 in each expansion or something, even though the question doesn't specify it)

I am showing my lack of understanding, and It's probably useless without specific examples. But If anyone can give some general tips, please do

 

[tommykins]

回复: Binomial

general tips include subbing in x = -1, 0 or 1
integrating and differentiating each side.

 

[midifile]

Re: 回复: Binomial

If the thing you are trying to prove is along the lines of:
Something = ⁿC₁ + 2ⁿC₂ + 3ⁿC₃ + 4ⁿC₄ + ... + nⁿC_n, where the number in front of the C thingo is the same as the little number on the bottom right of the C, it is likely that you have to differentiate to get the answer

If you are trying to prove:
Something = ⁿC₁/2 + ⁿC₂/3 + ⁿC₃/4 ... where the number on the denominator is 1 greater than the little number next to the C it is likely that you have to integrate.

But when you integrate, dont forget about adding a C at the end. You can usually work out what C is by letting x=0

Also if negative and positive signs alternate between terms, you usually have to sub in -1

 

[laureese]

i got told whenever it has fractions, you integrate