Show that If m > 1, then the sum of the mth powers of underline (n)even numbers is greater than n (n + 1)^m

Question

Show that If m > 1, then the sum of the m^th powers of n even numbers is greater than n (n + 1)^m.

Answer 1

Since m > 1, using the property: 

AM of mth power of n quantities > mth power of the AM of n quantities, we have

⇒ 2^m + 4^m + 6^m + .... (2n)^m > n (n + 1)^m.