abcalphaomega

thanks a million this was exactly what i was looking for.

yes i tried looking at df/dn. i dont see why the expression must be greater than 0 for n>1. its not very neat as it is.

yes, this exactly...

sorry was in a bit of hurry last time. am-gm means AM- GM inequality similarly AM - quadratic mean (am-qm)inequality. the function is a variable of n. im simply looking for a proof of f(n)= [ a^n +b^n + c^n / 3 ]^(1/n) is monotonically increasing for n>1. eg. f(2)>f(1) implies AM-QM. also i might add a,b,c are positive real nos. incidentally i stumbled upon the need for such an inequality in trying to prove that for a given volume sphere has minimum surface area. something often told in fluid mechanics classes. i will be done with the proof if i find an analogous proof as that of the above inequality only involving averaged integration of a function rather than mean of discrete quantities.

can someone pls give me a link or some proof of why the function [(a^n+b^n+c^n)/3]^1/n is monotonically increasing for n>1. i can see that am-gm, am-qm etc follow from this fact. also pf for mean of k nos will be preferable than for 3 stated above. also can i replace sigma ain / k by (definite integral from a to b xn dx) / b-a in the above inequality??