anonymous
  • anonymous
Find a power series representation for the function f(x)= 2/(1-2x). For what values of x does it equal the function?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
You can take the Taylor Series Expansion, but I am not so sure what you mean by for what values of x does it equal the function. In theory all values of x should equal the function so long as the series converge.
anonymous
  • anonymous
Taylor Expansion at center x=0 would be 2+4 x+8 x^2+16 x^3+32 x^4+64 x^5+..
anonymous
  • anonymous
Hmm. Well the geometric progression a+ax^2+ax^3... converges to a/(1-x) when -1

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anonymous
  • anonymous
Hmm...i think i get what you mean
anonymous
  • anonymous
Should be a+ax+a(ax)^2+a(ax)^3... Missed the x term all over lol
anonymous
  • anonymous
Sigh. Well the geometric progression a+ax+ax^2+ax^3... converges to a/(1-x) when -1
anonymous
  • anonymous
so how did you come up w/ it converging to a/(1-x)
anonymous
  • anonymous
Its a geometric series. It's derived without calculus. It goes: Let a=1+x+x^2+x^3... So ax=x+x^2+x^3... a-ax=1. So a=1/(1-x) I said it only converges for -1
anonymous
  • anonymous
ok thanks so much! :)
anonymous
  • anonymous
Np

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