Binomial Help PLS (1 Viewer)

pencilspanker

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Hey guys having heaps of trouble with binomial, would be great if someone could help with this question!
https://gyazo.com/e0b5251a4a6f2123f58967e4d7049c04
Thanks.
FYI I think the result in ii) you will get n(n-1)2^n-2 i think that is correct atleast thats what i got maybe the question is written wrong
But anyways i need help with iii) just dont know how to start
 

InteGrand

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ichila101

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for part iii) to start off you are proving mathematical induction so you can start with proving the left side = right side by substituting n = 4 to both sides then go on from there.

a hint for part ii) is to look carefully at the expression and remember you are differentiating with respect to 'x' for the expression n*x*(1+x)^(n-1)
 

integral95

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for part iii) to start off you are proving mathematical induction so you can start with proving the left side = right side by substituting n = 4 to both sides then go on from there.

a hint for part ii) is to look carefully at the expression and remember you are differentiating with respect to 'x' for the expression n*x*(1+x)^(n-1)
You don't use mathematical induction in HSC unless otherwise stated.

in iii), you differentiate part i) again, then multiply both sides by x, sub x = -1, then add this with part ii) then divide by 2.
 

ichila101

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You don't use mathematical induction in HSC unless otherwise stated.

in iii), you differentiate part i) again, then multiply both sides by x, sub x = -1, then add this with part ii) then divide by 2.
My mistake

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