The discussion revolves around finding the sum of the first n terms of a sequence denoted as U1, U2, U3, etc. The specific nature of the sequence is not clearly defined, leading to questions about its terms and behavior.
There is ongoing exploration of the sequence's properties, with some participants providing insights into the behavior of the sum. Multiple interpretations of the sequence are being considered, and guidance has been offered regarding the formulation of the sum.
Participants note the lack of clarity regarding the sequence's terms and the assumptions being made about its behavior. The discussion reflects uncertainty about the exact nature of the problem and the definitions involved.
What are U1, U2, etc.?lionely said:Homework Statement
Find the sum of the first n terms of the sequence U1, U2, U3... Ur
lionely said:Homework Equations
The Attempt at a Solution
$$ \sum_{r = 1}^n (1 + (-1)^r) = n + (-1)^n $$
But I don't this is right... any help?
Like before, write out the first few terms of the series.lionely said:It doesn't say this is the exact question, it just wants me to find the Sum of the first n terms of this case
You said, "It" alternates ...lionely said:It alternates between 1 and -1 so would the sum would alternate between -1 and 0... so... 1/2( (-1)^n -1) ?
lionely said:when I mean "it" I meant the sequence. I'm sorry and what I typed above was in reference to the part I did not understand, the sum of (-1)^n. I understand the sum of 1 to n terms = n.
so my final answer is $$ n + 1/2((-1)^n -1)$$