Question

Sum of the mth powers of n even numbers is $>n(n+1{)}^m$ if m > 1

• A. True
• B. False

Answer 1

The correct option is A True

$\frac{2^m+4^m+\dots \dots (2n{)}^m}{n}>{\left(\frac{2+4+6+\dots \dots 2n}{n}\right)}^m$
or $2^m+4^m+\dots \dots (2n{)}^m>n{\left(\frac{2.n(n+1)}{2n}\right)}^m$
or $>n(n+1{)}^m$ $\because \sum n=\frac{n(n+1)}{2}$