Question

(please see attachment). POWER SERIES, REPRESENTATION.

Answer 1

How did they get from the first line to the second?

Answer 2

The first term on line 1 can be expanded to give the first two terms on line 2. So I don't think line 2 is correct. I think you're missing an x.

Answer 3

I see what they have done now.

Answer 4

\[\sum_{n=0}^{\infty} x ^{n+1} = x + \sum_{n=1}^{\infty} x ^{n+1}\]

Answer 5

x^0 = 1 ... seems all right!!

Answer 6

I'm too slow with the equation editor. But as I say, the first term on line 1 expands to the first two terms on line 2. The second term on line 1 expands as above. There needs to be another x on line 2.

Answer 7

Oh.. see a problem now

Answer 8

Need to factor out another x from each term of the second series. I'm not sure you can do that.

Answer 9

assuming x != 0