# Toronto Math Forum

## MAT334--2020S => MAT334--Lectures & Home Assignments => Chapter 2 => Topic started by: Yan Zhou on February 10, 2020, 04:42:13 PM

Title: 2.2 home assignment question 18
Post by: Yan Zhou 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.

Title: Re: 2.2 home assignment question 18
Post by: Victor Ivrii on February 11, 2020, 07:38:13 AM
Please correct what you typed
Title: Re: 2.2 home assignment question 18
Post by: Yan Zhou 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 $1+i$".
Title: Re: 2.2 home assignment question 18
Post by: Victor Ivrii on February 12, 2020, 03:12:59 PM
Fixed. Thanks!