Suppose [x] denote the greatest integer ≤x and n∈N, then limn→∞  nCox2+ nC1x2+⋯+ nCnx22n−2 is equal to

# Suppose [x] denote the greatest integer $\le x$ and $n\in \mathbf{N}$, then  is equal to

1. A

$\frac{1}{2}{x}^{2}$

2. B

${x}^{2}$

3. C

$2{x}^{2}$

4. D

$4{x}^{2}$

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### Solution:

We know $x-1<\left[x\right]\le x\mathrm{\forall }x\in \mathbf{R}$, there fore

Taking limit as $n\to \mathrm{\infty }$ ,and using sandwich theorem, we get

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