Question

For n > 2 , the AM of the first n natural numbers is greater than n +1.
Is the statement true or false?
Give justification in support of your answer.

Answer 1

Answer on Question #79105 – Math – Linear Algebra

Question

For $n > 2$, the AM of the first $n$ natural numbers is greater than $n + 1$.

Is the statement true or false?

Give justification in support of your answer.

Solution

The sum of first $n$ natural numbers is $n(n+1)/2$.

So, arithmetic mean of first $n$ natural numbers is $(n+1)/2$ which is less than $n+1$.

So, the statement is false.

Answer: the statement is false.

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