MAT334--2020S > Chapter 2

2.2 home assignment question 18

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**Yan Zhou**:

Find the closed form for the given power series.

$$\sum_{n=2}^{\infty}n(n-1)z^{n}$$

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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