JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

C_0, C_1, C_2, \cdots, C_n

are binomial coefficients, then

\lim \limits_{{n \rightarrow \infty}}\left[C_n-\left(\frac{2}{3}\right) C_{n-1}+\left(\frac{2}{3}\right)^2 C_{n-2}+\cdots+(-1)^n\left(\frac{2}{3}\right)^n C_0\right]

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Correct option: A

Option A (0) is the correct answer because the limit of the given expression as n approaches infinity is 0.

More Questions from BINOMIAL THEOREM

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\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

d

\left( {n + 1} \right)

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

(1-x)^{201}\left(1+x+x^2\right)^{200}

\left(\frac{1}{x}+2 x\right)^n

{x^5}

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n