A) \[\frac{pq}{r}\]
B) \[{{e}^{\frac{pq}{r}}}\]
C) 0
D) 1
Correct Answer: C
Solution :
\[S={{(p+q+r)}^{n}}\]\[\{Putting\,x=y=z=1\}\] |
\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{S}{{{({{S}^{1/n}}+1)}^{n}}}=\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{(p+q-r)}^{n}}}{{{\{(p+q-r)+1\}}^{n}}}\] |
\[\underset{n\to \infty }{\mathop{\lim }}\,{{\left( \frac{p+q-r}{(p+q-r+1)} \right)}^{n}}=0\] |
\[\left\{ as\left( \frac{p+q-r}{(p+q-r+1)} \right)<1 \right\}\] |
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