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When the terms in the binomial expansion of \left(\sqrt{x}+\frac{1}{2 \sqrt[4]{x}}\right)^n are arranged in decreasing powers of x, the coefficients of the first three terms are in A.P. The number of terms in the expansion with integer powers of x is

 

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

$$ \begin{aligned} & 1+\frac{n_{C_2}}{4}=2\left(\frac{n_{C_1}}{2}\right)_{\text {gives } \mathrm{n}}=8 \\ & \therefore T_{r+1}=8 C_r\left(\frac{1}{2}\right)^r x^{(16-3 r) / 4} \Rightarrow 4 / 16-3 r \end{aligned} $$ for $r=0,4$ and 8 only

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Kshitij

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