past paper help? (1 Viewer)

angrycatnoises · Sep 13, 2016

with part ii) mainly. My math teacher is currently stuck as well

InteGrand · Sep 13, 2016

InteGrand said:
$\noindent Assuming you got part i), we have $\sum _{r=1}^{n}\left(1+x\right)^{r-1} = \sum _{r=1}^{n} \binom{n}{r}x^{r-1}$. The fact we are asked to prove follows immediately by equating coefficients of $x^{2}$ of both sides of the part i) identity. Note that coefficient of $x^{2}$ on the L.H.S. in part (i) is $\sum_{r=1}^{n}\binom{r-1}{2} = \sum_{r=2}^{n-1}\binom{r}{2}$.$

$\noindent Assuming you got part i), we have $\sum _{r=1}^{n}\left(1+x\right)^{r-1} = \sum _{r=1}^{n} \binom{n}{r}x^{r-1}$. The fact we are asked to prove follows immediately by equating coefficients of $x^{2}$ of both sides of the part i) identity. Note that coefficient of $x^{2}$ on the L.H.S. in part (i) is $\sum_{r=3}^{n}\binom{r-1}{2} = \sum_{r=2}^{n-1}\binom{r}{2}$.$

InteGrand · Sep 13, 2016

past paper help? (1 Viewer)

angrycatnoises

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InteGrand

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InteGrand

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