### Author Topic: 2.2 home assignment question 18  (Read 733 times)

#### Yan Zhou

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•   • Posts: 15
• Karma: 1 ##### 2.2 home assignment question 18
« on: February 10, 2020, 04:42:13 PM »
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.

« Last Edit: February 12, 2020, 12:37:46 PM by Yan Zhou »

#### Victor Ivrii ##### Re: 2.2 home assignment question 18
« Reply #1 on: February 11, 2020, 07:38:13 AM »

#### Yan Zhou

• Full Member
•   • Posts: 15
• Karma: 1 ##### Re: 2.2 home assignment question 18
« Reply #2 on: February 12, 2020, 12:36:51 PM »
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 ##### Re: 2.2 home assignment question 18
« Reply #3 on: February 12, 2020, 03:12:59 PM »
Fixed. Thanks!