Well, I just need a little help in these... There are parts that I can't completely understand:
Find the complete interval of convergence for each series
For this one... All I could do was set up the limit for the ratio test:
For this one, I did a bit of work... But I need to know something:
This supposedly equals:
But I don't really know how the limit gets to 1.
Any help is appreciated.
Thanks that helped quite a bit.
I'm going to go ahead and finish that one and see if the rest of it is right:
For x = -6:
The alternating series converges because:
Therefore converges at x = -6.
For x = -4:
This would lead to the same series, meaning that the sum converges for x = -4 as well.
Is that it?
These series are quite confusing, our teacher never told us the behavior of series with natural logarithms, for example:
When x = -1 it gives an alternating series, supposedly it converges, but I can't prove it necessarily since the first term of it is 0 and the second term is . Of course only the absolute value of it matters, but the terms in the sequence decrease only when ... Does that still imply convergence?