Every term is even and the signs alternate.
Using is a standard way to alternate signs.
Pattern recognition is the most important skill you can have to help you.
Next step is to try to find a pattern.
We see that the signs alternate, suggesting that there is a term in this sequence. Since the first term is negative, and we're starting from k=1 (which is an odd number), we see that the sequence will include a .
Now, what is the kth term of the sequence ?
We note that this is the sequence of even numbers. and we know that ; this suggests that the kth term is .
We can now see that this sum can be expressed as follows:
Does this make sense?
EDIT: Plato beat me. As he mentioned, pattern recognition is very important!!
Ok, i kinda see where your going. Whats the difference, because one of you has , and the other has (-1)^(k+1) is there any difference? I have a test today, and this will be on it, and I was looking at my notes, trying to figure out a way to do these, but this helps.
Oh yeah, also say teh numbers were switched, like 2-4+6-8+10, then it would still be k=1 to 5, then sigma *2k ?