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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