Have you noticed that ?
I'm studying for my final and my teacher gave me a worksheet. I have two sequence problems I do not understand at all. If anyone could please help I'd appreciate it!
1. Find the sum of the sequence, note i=symbol for factorial, I couldn't find a factorial symbol :
((2n-1)i) / ((2n+1)i)
2. find sum of sequence (That's exactly how written, I have no idea...) :
2, -1/2 + 1/8 - ... 1/2048
"fully evaluated" means nothing.
Finding a parsimonious expression for a sum can be an art. Wonderful accolades have been awarded because of such discoveries. Other than self-awesomeness, though, you need a bag of references. In this case, notice further that:
Write out the expression for n = 1, 2, and 3 and see if you notice anything. (Resist the temptation to add anything.)
You probably should differentiate between a sequence (a list) and a series (add things up).
Did you list the terms associated with n = 1, 2, and 3? Really, it will be quite enlightening. You will fail this course if you can't list three terms of a series.
n = 1 leads to
How about n = 2?
Note: That ratio on #2 looks like "-1/4" and it appears to be finite.
Telescoping series - Wikipedia, the free encyclopediaNever noticed that, how did you get it? and how does that lead to the sum?