If $m > 1$ and $n \in N$, then

$\frac{1^m+2^m+3^m+\ldots+n^m}{n} \geq 1$

$\frac{1^m+2^m+3^m+\ldots+n^m}{n} \leq 1$

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Medium

1 of 1

Analyzing +4 | -1

m > 1

and

n \in N

, then

View answer and explanation

Correct option: A

\frac{1^m+2^m+3^m+\ldots+n^m}{n} > \left(\frac{n+1}{2}\right)^m

Option A is correct because for m > 1, the Arithmetic Mean of mth power is greater than the mth power of the Arithmetic Mean.

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