The r^{th} term in the expansion of (a + 2x)^ | vedclass

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(B) The general term formula for the expansion of $(a + b)^n$ is $T_{r+1} = ^nC_r a^{n-r} b^r$.To find the $r^{th}$ term,we substitute $r$ with $r-1$

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$\frac{n(n - 1)...(n - r + 2)}{(r - 1)!} a^{n - r + 1} (2x)^{r - 1}$

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(B) The general term formula for the expansion of $(a + b)^n$ is $T_{r+1} = ^nC_r a^{n-r} b^r$.To find the $r^{th}$ term,we substitute $r$ with $r-1$ in the general term formula:$T_r = T_{(r-1)+1} = ^nC_{r-1} a^{n-(r-1)} (2x)^{r-1}$$T_r = ^nC_{r-1} a^{n-r+1} (2x)^{r-1}$Using the definition of combinations,$^nC_{r-1} = \frac{n!}{(n-r+1)!(r-1)!} = \frac{n(n-1)...(n-r+2)}{(r-1)!}$.Thus,$T_r = \frac{n(n-1)...(n-r+2)}{(r-1)!} a^{n-r+1} (2x)^{r-1}$.

The $r^{th}$ term in the expansion of $(a + 2x)^n$ is

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