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  • If the seventh terms from the beginning and the end in the expansion of(√(3&2)+1/√(3&3))^n are equal, then n equals _________________

If the seventh terms from the beginning and the end in the expansion of \left ( \sqrt[3]{2} + \frac{1}{\sqrt[3]{3}}\right )^{n}   are equal, then n equals _________________

Answers (1)

Given: \left ( \sqrt[3]{2} + \frac{1}{\sqrt[3]{3}} \right )^{n}

Now, referring to que 14.

\frac{^{n}C_{6} \left ( \sqrt[3]{2} \right )^{n-6}\left ( \frac{1}{\sqrt[3]{3}} \right )^{6}}{^{n}C_{6}\left ( \frac{1}{\sqrt[3]{3}} \right )^{n-6}\left ( \sqrt[3]{2} \right )^{6}}=1

Thus

\frac{\left ( \sqrt[3]{2} \right )^{n-12}}{\left (\frac{1}{\sqrt[3]{3} }\right )^{n-12}}=1

Thus 

6(n-12)/3 = 60

(n-12)/3 = 0

Thus, n = 12
 

Posted by

infoexpert22

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