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Question: How can I find n so that maximum of all coefficients of the expand (1+2x)^n is a8?

Question:How can I find n so that maximum of all coefficients of the expand (1+2x)^n is a8?

toandhsp 305
June 27 2014
2

Suppose (1 + 2x)^n = a0 + a1*x + a2*x^2+...+an*x^n.

I want to find value of n so that max(a0, a1, ..., an) is a8. 

I tried directly. 

With n = 12. 

restart:
A:=expand((1+2*x)^12,x);
max(coeffs(A));

And with n = 11. 

B:=expand((1+2*x)^11,x);
max(coeffs(B));


Therefore,  n = 12 or  n = 11. 

How can I solve the problem with Maple?
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