- #1
chipotleaway
- 174
- 0
I'm having trouble the underlined red part of this proof (attached image) of the what looks to be the alternate series test, not sure if it's an error but it's more likely I've perhaps misunderstood something.
If y_j is defined as the sequence of partial sums of the even terms of the sequence x_j from j=n onwards (i.e. the positive terms), then shouldn't y_{j+1}=y_j + x_{N+2j+2}?
How does x_{N+2j+1} come in? Thats an odd/negative term of x_N!
And then the result is that y_j \geq y_{j+1}, but but if y_j[/tex] is the sequence of positive partial sums, then should it not be increasing?
If y_j is defined as the sequence of partial sums of the even terms of the sequence x_j from j=n onwards (i.e. the positive terms), then shouldn't y_{j+1}=y_j + x_{N+2j+2}?
How does x_{N+2j+1} come in? Thats an odd/negative term of x_N!
And then the result is that y_j \geq y_{j+1}, but but if y_j[/tex] is the sequence of positive partial sums, then should it not be increasing?
