Binomial Help PLS (1 Viewer)

pencilspanker · Nov 12, 2018

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 · Nov 12, 2018

pencilspanker said:
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

$\noindent By the way, the answer to ii) can't be $n(n-1)\cdot 2^{n-2}$. If this was the case, then substituting $n=1$ into your answer gives $0$, so the series would have to equal $0$ when $n=1$. But clearly when $n=1$, the series equals $\binom{1}{1}1^{2} = 1 \color{red}\neq\color{black} 0$.$

pencilspanker · Nov 12, 2018

InteGrand said:
$\noindent By the way, the answer to ii) can't be $n(n-1)\cdot 2^{n-2}$. If this was the case, then substituting $n=1$ into your answer gives $0$, so the series would have to equal $0$ when $n=1$. But clearly when $n=1$, the series equals $\binom{1}{1}1^{2} = 1 \color{red}\neq\color{black} 0$.$

welp gg fuk got ii) wrong as welll yayy

ichila101 · Nov 12, 2018

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 · Nov 14, 2018

ichila101 said:
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 · Nov 14, 2018

integral95 said:
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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Binomial Help PLS (1 Viewer)

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