Is this statement true?

  • Thread starter cstvlr
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  • #1
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Main Question or Discussion Point

int x^n from 0 to 1 = 1/(n + 1)

But as n approaches infinity the answer becomes zero.
 

Answers and Replies

  • #2
Char. Limit
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Yep. And if you look at x^n for some number 0<x<1 and 0<n, x^n will get smaller as n increases. It's only natural to see the integral get smaller as well.
 
  • #3
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Ok, thanks.
 
  • #4
Mute
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int x^n from 0 to 1 = 1/(n + 1)

But as n approaches infinity the answer becomes zero.
It is true as long as [itex]n > -1[/itex]. For n < 0, it is not true.
 
Last edited:
  • #5
D H
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It is true as long as [itex]n \geq 0[/itex]. For n < 0, it is not true.
Correction: It is true as long as n > -1, not zero.
 
  • #6
Mute
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Correction: It is true as long as n > -1, not zero.
Corrected. Thanks. I forgot to edit that when I decided not to talk only about integers.
 

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