SOLUTION: Show that n <= 1 +sqrt(2)+sqrt(3)+...+sqrt(n) <= n(n+1)/2

Question 990264: Show that n <= 1 +sqrt(2)+sqrt(3)+...+sqrt(n) <= n(n+1)/2
Answer by ikleyn(52792)   (Show Source): You can put this solution on YOUR website!
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Show that n <= 1 + + + . . . + <=
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It is very easy.

First, n <= 1 + + + . . . + .

Replace every    by the smaller quantity of 1, and you will get this inequality.

Second, 1 + + + . . . + <= .

Replace every    by the greater quantity of k, and you will get this inequality. (You will have the sum of first n natural numbers which is exactly ).

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