anonymous
  • anonymous
Anyone know how to write the power series of the constants 0 and 1. 0+0+0+0 and 1+0+0+0, are those even power series?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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KingGeorge
  • KingGeorge
Those are not power series. A power series is of the form \[\large \sum_{n=0}^\infty a_n x^n.\]To write the power series for 0 and 1, you need to figure out how to write them in this form.
KingGeorge
  • KingGeorge
For example, to write the power series of 0, you might say \[\large \sum_{n=0}^\infty 0x^n.\]I'll let you handle the way to write 1.
anonymous
  • anonymous
Alright thanks for that. Thinking have to make all the x's add to one.

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KingGeorge
  • KingGeorge
It's simpler than that. The x's should be able to be any. For example, if you put in x=googol, then it should still equal 1. Or if x=-googol.
anonymous
  • anonymous
Now I am thinking it has to do with the x in X^n. But if that changed from 0 to infinity... Don't think it is the a_n.
anonymous
  • anonymous
I mean the n in x^n
anonymous
  • anonymous
Glad I have time to think about this. Guess I should have been able to do the 0.
KingGeorge
  • KingGeorge
Let me know if the series for 1 gives you more trouble. I assure you, it's simpler than you're thinking :)
anonymous
  • anonymous
Ok, thanks I am setting the series equal to one and hoping that is a step in the right direction.
KingGeorge
  • KingGeorge
Consider writing the series as \[1=a_0+a_1x+a_2x^2+...\]
anonymous
  • anonymous
Sorry for the trouble. Given that and if x can be anything. then a_0 =1 and a_1 to a_infinity are 0?
KingGeorge
  • KingGeorge
That's it.
anonymous
  • anonymous
Awesome. Thanks!
KingGeorge
  • KingGeorge
You're welcome.

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