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?

Question

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?

kinggeorge · Answer

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 · Answer

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 · Answer

Alright thanks for that. Thinking have to make all the x's add to one.

kinggeorge · Answer

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 · Answer

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 · Answer

I mean the n in x^n

anonymous · Answer

Glad I have time to think about this. Guess I should have been able to do the 0.

kinggeorge · Answer

Let me know if the series for 1 gives you more trouble. I assure you, it's simpler than you're thinking :)

anonymous · Answer

Ok, thanks I am setting the series equal to one and hoping that is a step in the right direction.

kinggeorge · Answer

Consider writing the series as $$1=a_0+a_1x+a_2x^2+...$$

anonymous · Answer

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 · Answer

That's it.

anonymous · Answer

Awesome. Thanks!

kinggeorge · Answer

You're welcome.