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Problem 11 Easy Difficulty

Find the Maclaurin series for $ f(x) $ using the definition of a Maclaurin series. [ Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0. $] Also find the associated radius of convergence.

$ f(x) = (1 - x)^2 $

Answer

$f(x)>1-2 x+\frac{2}{2!} x^{2}, \quad R=\infty$

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Video Transcript

so fun. The connoisseurs for FX using a definition of mech Lauren Siri's all right. So the definition of it is going to be. And from zero to infinity, the doing of half at zero. Over in factorial, Tom's ex called in. Okay, so after X equals two Woman is a square. So after zero equals one and I front of X on at zero, it's going to be on two times women's likes and no one at zero. So this is just Teo minus two and the second your video a zero is going to be so this part, it's ah, pleased to X minus two. Do it here and Cyril in just two. And you see the first, the first third directive is gonna be zero and so on is going to zero. So you have only three times for every thanks. The first time is some one times extreme help zero, which is one class is minus two axe blows. Teo Victoria Square, which is just one wants to expose. It's where so you see, we just expand this square, their equivalent Oh, the horses. Just the whole realize of this infinity

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