(please see attachment). POWER SERIES, REPRESENTATION.

Question

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

I see what they have done now.

anonymous · Answer

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

experimentx · Answer

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

anonymous · Answer

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.

anonymous · Answer

Oh.. see a problem now

anonymous · Answer

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

experimentx · Answer

|dw:1343493277687:dw|
assuming x != 0