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zZ
Numerade Educator

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Problem 2 Easy Difficulty

Suppose you know that the series $ \sum_{n = 0}^{\infty} b_n x^n $ converges for $ \mid x \mid < 2. $ What can you say about the following series? Why?
$ \sum_{n = 0}^{\infty} \frac {b_n}{n + 1} x^{n + 1} $

Answer

The series $$\sum_{n=0}^{\infty} \frac{b_{n}}{n+1} \cdot x^{n+1}$$ converges and interval of comvergence is $|x|<2$

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Video Transcript

to do this problem. They also need to use the same techniques that they used in problem one that is racial types. So first they set a tone Iko too nice, serious on DH. They want to use ah racial test Saturday night. We know it's a serious converge as Lee meet absolute value of eight and castle and oh, and should be smaller, the land And in this case, a any goto be in times ax to the power. So what do we got? A CZ absolute value B and class one two times ax to the power and class one Oh, uh a A and times X to the power and absolute value. Smaller man. So this is your creation. We can eliminate it once the cat is Of course, they made go to infinity. Me and Class one Oh, a B and Times X is smaller than so. What they know is radios off. Convergence of a m, eh Axe. Absolute values more than two. So I slow as we choose x Absolutely smaller too. So how serious is it? The serious as come watch. So what we got is Hey, mate. Ah on go to the infinity, B and classmen. Oh, a B N should be in Kyoto, huh? Only in this case we get these radios off. Convergence two we are then.