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  • If the sum of the coefficients in the expansion of <img alt="(1+2 x)^n \text { is } 6561" src="https://entrancecorner.oncodecogs.com/gif.latex?%281&plus;2%20x%29%5En%20%5Ctext%20%7B%20is%2

If the sum of the coefficients in the expansion of (1+2 x)^n \text { is } 6561 , the greatest term in the expansion at x=1 / 2 \text { is }

Option: 1

4^{t h}


Option: 2

5^{t h}


Option: 3

6^{t h}


Option: 4

none of these


Answers (1)

best_answer

Sum of the coefficients in the expansion of (1+2 x)^n=6561

\begin{array}{ll} \Rightarrow & (1+2 x)^n=6561, \text { when } x=1 \\ \Rightarrow & 3^n=6561 \\ \Rightarrow & 3^n=3^8 \Rightarrow n=8 \end{array}

Now, m=(n+1) \frac{|2 x|}{1+|2 x|}=\frac{9}{2}=4.5

Hence, 5^t^h term is the greatest term. 

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Anam Khan

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