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7.Binomial Theorem
medium
${r^{th}}$ term in the expansion of ${(a + 2x)^n}$ is
A
$\frac{{n(n + 1)....(n - r + 1)}}{{r!}}{a^{n - r + 1}}{(2x)^r}$
B
$\frac{{n(n - 1)....(n - r + 2)}}{{(r - 1)\,!}}{a^{n - r + 1}}{(2x)^{r - 1}}$
C
$\frac{{n(n + 1)....(n - r)}}{{(r + 1)!}}{a^{n - r}}{(x)^r}$
D
None of these
Solution
(b) ${r^{th}}$ term of ${(a + 2x)^n}$ is $^n{C_{r – 1}}{(a)^{n – r + 1}}{(2x)^{r – 1}}$
$ = \frac{{n!}}{{(n – r + 1)!(r – 1)!}}{a^{n – r + 1}}{(2x)^{r – 1}}$
$ = \frac{{n(n – 1)…..(n – r + 2)}}{{(r – 1)!}}{a^{n – r + 1}}{(2x)^{r – 1}}$
Standard 11
Mathematics
