MAT334--2020S > Chapter 2

2.2 home assignment question 18


Yan Zhou:
Find the closed form for  the given power series.


hint: divide by $z^{2}$

I tried the hint but still have no idea.

Thanks in advance.

Victor Ivrii:
Please correct what you typed

Yan Zhou:
Yes, I just find out that it is different from textbook, and I know how to do it now.
By the way, there is a typo in question 16 which should be $$\sum_{n=1}^{\infty} n(z-1)^{n-1}$$ instead of $$\sum_{n=1}^{\infty} (z-1)^{n-1}$$

In section 2.3,
question 5 should be $$\int_{0}^{2\pi} \frac{d\theta}{2+cos\theta}$$ instead of $1+cos\theta$
question 8 should be $$\int_{0}^{\pi}\frac{d\theta}{1+(sin\theta)^2}$$ the range is from 0 to $\pi$ instead of $2\pi$
question 9 should be "joining $1-i$ to $1+i$".

Victor Ivrii:
Fixed. Thanks!


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