Re: series
From: José Carlos Santos (jcsantos_at_fc.up.pt)
Date: 07/14/04
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Date: Wed, 14 Jul 2004 10:41:34 +0100
mina_world wrote:
> Assume f : [1,00) -> R is continuous,
>
> nonnegative, decreasing and
>
> sigma f(k) is convergent.
> k=1~00
>
> then
>
> integral f(x) dx <= sigma f(k) [1~00]
> 1~00
>
> ------------------------------
> it's true ??
Yes, it's true, because, since f is decreasing,
integral f(x) dx <= f(1)
1 <= x <= 2
integral f(x) dx <= f(2)
2 <= x <= 3
and so on.
Best regards,
Jose Carlos Santos
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