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Question

If the sum of the coefficients in the expansion of $${(x+y)}^{n}$$ is $$4096$$, find the greatest coefficient in the expansion.


Solution

Sum of all the coefficient of $$(x+y) ^{ n }$$ is $$4096$$

Sum $$={ 2 }^{ n }=4096$$

When $$ x=1$$ and $$y=1$$

So $$ n=12$$.

[Note: Greatest Coefficient of $$ (1+x) ^{ n }$$ is the Coefficient of Middle 

Term $$ ^{ n }C_{\frac{n}{2} }$$, if $$n$$ is even and if $$n$$ is odd then $$^{ n }C_{\frac{(n+1)}{2}}$$ or $$^{ n }C_{\frac{(n-1)}{2}}]$$

So, the greatest coefficient is $$^{ 12 }C_{ 6 }=924$$.

Mathematics

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