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[tex] f(x) = 1 + x + x^2 = 7 + 5 (x-2) + (x-2)^2 [/tex]

which is a Taylor series centered at 2. My question is: what is the radius of convergence? The answer in my book is [tex] R=\infty [/tex], but take a look at this:

[tex] f(x) = 7 + 5 (x-2) + (x-2)^2 = \sum _{n=0} ^{\infty} b_n (x-2)^n \Longrightarrow \left| x-2 \right| < 1 [/tex]

Then, I get

[tex] 1 \leq x \leq 3 \Longrightarrow R = \frac{3-1}{2}=1 \neq \infty [/tex]

In other words, I'm a bit confused!

Thanks

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# Homework Help: Taylor Series/Radius of Convergence - I just need a hint!

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