JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

1 of 1

Application +4 | -1

\lambda=\frac{1 \times 2^2+2 \times 3^2+3 \times 4^2+\ldots \text { upto } 99 \text { terms }}{1+2+3+\ldots \text { upto } 100 \text { terms }}

then

\lambda

equals

View answer and explanation

Correct option: A

4983

Option A (4983) is correct because after simplifying the summation, we get

\frac{{n(n+1)}}{{2}} - \frac{{2n+1}}{{3}}

which equals 4983 when n=100.

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