JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Analyzing +4 | -1

\sum\limits_{{r=0}}^{2 n} a_r(x-2)^r=\sum\limits_{{r=0}}^{2 n} b_r(x-3)^r

and

a_k=\frac{1}{{ }^{n+k} C_n}

for

0 \leq k \leq n

then

b_n

equals

View answer and explanation

Correct option: D

n+1

Option D (

n+1

) is correct because by substituting

x-3=t

, the coefficient

b_n

is found to be the sum of

a_k { }^{n+k} C_k

from k=0 to n, which simplifies to

n+1

More Questions from BINOMIAL THEOREM

Practice All Chapter MCQs →

\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