If s be the sum of the coefficients in the expansion of $(p x + q y + r z)^{n}, p, q, r > 0$ , then ${lim}_{n \to \infty} \frac{S}{(S^{\frac{1}{n}} + 1)^{n}}$ =

pq/r

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e ^pq/r

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None

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Solution

The correct option is C
0

$s = (p + q + r)^{n} \Rightarrow \frac{s}{(s^{\frac{1}{n}} + 1)^{n}} = (\frac{p + q + r}{p + q + r + 1})^{n}$
$\frac{p + q + r}{p + q + r + 1} < 1 \Rightarrow {lim}_{n \to \infty} \frac{s}{(s^{\frac{1}{n}} + 1)^{n}} = 0$

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