If 1 - xn - C0n - C1nx- C2nx2 - - - Cnnxnthen the value of C0n - 3 C1n - 9 C2n- - - 3n Cnnis

If we substitute x=3 in the above expression, we get nbsp;(1 nbsp;+ nbsp;3)n nbsp;= nbsp; nbsp;C0n nbsp;30 nbsp;+ nbsp; nbsp;C1n nbsp;31 ...

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General Term of Binomial Expansion

If 1 + xn = C...

Question

$If {(1 + x)}^{n} = n C 0 + n C 1 x + n C 2 x^{2} + . . . + n C n x^{n} then the value of n C 0 + 3 n C 1 + 9 n C 2 + . . . + 3^{n} n C n is$
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2^{n}

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3^{n}

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2^{n - 1}

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4^{n}

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Solution

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If {(1 + x)}^{n} = n C 0 + n C 1 x + n C 2 x^{2} + . . . + n C n x^{n} then the value of n C 0 + 3 n C 1 + 9 n C 2 + . . . + 3^{n} n C n is

If {(1 + x)}^{n} = n C 0 + n C 1 x + n C 2 x^{2} + . . . + n C n x^{n} then the value of n C 0 + 3 n C 1 + 9 n C 2 + . . . + 3^{n} n C n is

lim x \to 3 \frac{x^{n} - 3^{n}}{x - 3} = 108

n

C (2 n, 3) : C (n, 2)

=

12 : 1

n

=

1, z_{1}, z_{2}, z_{3}, \dots z_{n - 1}

n

\frac{1}{3 - z_{1}} + \frac{1}{3 - z_{2}} + \dots + \frac{1}{3 - z_{n - 1}}

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