The coefficient of xr-0 - r - n-1- in the expression of x - 2n-1 - x-2n-2 -x-1 - x-2n-3- x-12-x-1n-1 is

The correct option is A ^nC_r(2^n r 1) Given expression is equal to ∑ _ p=1 ^ n (x+3) ^ (n p) × (x+2) ^ (p 1) #160;Which is equal to (x+3) ...

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General Term of Binomial Expansion

The coefficie...

Question

The coefficient of $x^{r} [0 \leq r \leq n - 1]$ in the expression of $(x + 2)^{n - 1} + (x + 2)^{n - 2} . (x + 1) + (x + 2)^{n - 3} . (x + 1)^{2} + . . . + (x + 1)^{n - 1}$ is

^{n} C_{r} (2^{r} - 1)

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^{n} C_{r} (2^{n - r} - 1)

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^{n} C_{r} (2^{r} + 1)

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^{n} C_{r} (2^{n - r} + 1)

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x^{r} (0 \geq r \geq n - 1)

(x + 2)^{n - 1} + (x + 2)^{n - 2} (x + 1) + (x + 2)^{n - 3} (x + 1)^{2} + . . . . . + (x + 1)^{n - 1}

^{n} C_{r} (2^{n - r} - 1)

x^{r} (0 \leq r \leq n - 1)

{(x + 2)}^{n - 1} + {(x + 2)}^{n - 2} \cdot (x + 1) + {(x + 2)}^{n - 3} \cdot {(x + 1)}^{2} + \cdot \cdot \cdot + {(x + 1)}^{n - 1}

x^{r} (0 \leq r \leq n - 1)

E = {(x + 2)}^{n - 1} + {(x + 2)}^{n - 2} (x + 1) + {(x + 2)}^{n - 3} {(x + 1)}^{2} + . . . . + {(x + 1)}^{n - 1}

x^{r} [0 \leq r \leq (n - 1)]

{(x + 3)}^{n - 1} + {(x + 3)}^{n - 2} (x + 2) + {(x + 3)}^{n - 3} {(x + 2)}^{2} + . . . . . + {(x + 2)}^{n - 1}

a_{0}, a_{1}, a_{2}

(1 + x + x

^{2})^{n}

f (x)

(r + 1) a_{r + 1} = (n - r) a_{r} + (2 n - r + 1) a_{r - 1}, (0 < r < 2 n)

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