JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Analyzing +4 | -1

Suppose

m

and

n

are positive integers and let

\begin{aligned} & S=\sum_{k=0}^n(-1)^k \frac{1}{k+m+1}\left({ }^n C_k\right) \\ & \text { and } T=\sum_{k=0}^m(-1)^k \frac{1}{k+n+1}\left({ }^m C_k\right) \text {, } \\ \end{aligned}

then

S-T

is equal to

View answer and explanation

Correct option: A

Option A (0) is correct because both S and T are equal to the Beta function B(m+1, n+1), making S-T = 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