thank you all]]>

Take a=1.2, b=0.00001, n=1

That gives (1.2+0.00001)^1.2*1</>(1.2^2)*1^0.00001, meaning 1.244...</>1.44.

So, in this case, a²*n^b is larger.

Almost all other cases result in (a+b)^na being larger.

e.g. (3+3)^3*1</>(3^2)*1^3, meaning 216</>9.

So, it can't be proven or disproven.

]]>contains two terms, among many, which are

a^a*n and b^a*n which appear to make the LHS greater than the RHS,

but when we assign arbitrary values,

say a=10, b=1,000,000,000 and n=100

the LHS is (1,000,000,010)^1000, which would contain 9,001 digits;

the RHS becomes

100 x (100^1,000,000,000) which would contain more than 2 billion digits!

This happened because we assumed b>>n.

Otherwise, the LHS may be greater.

Say, when a=10, b=100, n=1000.

LHS would be 110^10,000 containing 20,414 digits and the RHS would be much smaller, viz. 100*(1000^100), containing approximately 300 digits! ]]>

Perhaps we could start off with a proof for n=1, then onto 2 or perhaps n+1

]]>(a+b)^(n*a)>(a^2)(n^b)

:|

conditions:

a>0

b>0

n>=1

any help would be great

thnkx in advnc.