R th term in the expansion of a -2 x n isA- nn-1 -n-r-1-r - an-r-12 x-B- nn-1 -n-r-2-r-1 - an-r-12 x-1C- nn-1 -n-r-r-1 - an-rx-D- None of these

The correct option is B r^th term of (a+2x)^n is nbsp;^n C nbsp;_r 1(a)^n r+1(2x)^r 1 = nbsp; n!/(n r+1)!(r 1)! a^n r+1(2x)^r 1 = nbsp;n(n 1).....(n r ...

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Byju's Answer

Standard XII

Mathematics

General Term of Binomial Expansion

r th term in ...

Question

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

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None of these

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Solution

The correct option is B

$r^{t h}$ term of $(a + 2 x)^{n}$ is $^{n} C_{r - 1} (a)^{n - r + 1} (2 x)^{r - 1}$

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

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

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Similar questions

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

Q. Prove that:
(i)

\frac{n!}{(n - r)!}

= n (n − 1) (n − 2) ... (n − (r − 1))

(ii)

\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}

Prove that:
(i) $\frac{n!}{(n - r)!}$
= n(n-1)(n-2)...(n-(r-1))
(ii) $\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!}$
= $\frac{(n + 1)!}{r! (n - r + 1)!}$

Q. If

(1 - x)^{- n} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . . . . + a_{r} x^{r} + . . . . .

, then

a_{0} + a_{1} + a_{2} + . . . . . . + a_{r}

is equal to

Q. Sum of series

\sum_{r = 1}^{n} (r^{2} + 1) r!

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rth term in the expansion of (a+2x)n is

The correct option is B rth term of (a+2x)n is nCr−1(a)n−r+1(2x)r−1 = n!(n−r+1)!(r−1)!an−r+1(2x)r−1 = n(n−1).....(n−r+2)(r−1)!an−r+1(2x)r−1

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

The correct option is B

$r^{t h}$ term of $(a + 2 x)^{n}$ is $^{n} C_{r - 1} (a)^{n - r + 1} (2 x)^{r - 1}$

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

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