JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Hard

1 of 1

Analyzing +4 | -1

Let

S\left( k \right) = 1 + 3 + 5 + ... + \left( {2k - 1} \right) = 3 + {k^2}

. Then, which of the following is true?

View answer and explanation

Correct option: B

S\left( k \right) \Rightarrow S\left( {k + 1} \right)

Option B (

S(k) \Rightarrow S(k + 1)

) is correct because if we assume

S(k)

is true, then

S(k+1)

is also true, showing the implication holds.

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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