Okay, those are correct.

Why? What reason do you have to think that would work? For example, if I want to sum 2+ 8+ 9+ 11, the first number is 2, the last is 11, and there are 4 numbers. Their average, (2+11)/2, multiplied by 4 is 25. but the sum is actually 30.so I get

Now to evaluate the sum I take the (first term +last term)multiply by n and devide by 2.

Actually, I do know why you did that- for anarithmeticseries that is true, and a very useful fact. But it is trueonlyfor arithmetic series, where each term is the previous term plus a fixed number. For example, 2, 8, 14, 20, ... has each number the previous number plus 6. In the example I gave, 2+ 8+ 9+ 11, the second number is 2+ 6, but the third number is 8+ 1 and the fourth number is 9+ 2. Not a constant difference.

For your series, the first number is, as you say 1/2. The second number is 1/2- 1/3= 3/6- 2/6= 1/6 and the third number is 1/3- 1/4= 4/12- 3/12= 1/12.

1/3= 1/2+ (-1/6) but 1/12= 1/3+ (-3/12). NOT an arithmetic series.

Well, notThat gives me =

clearly Iám doing someting very very stupid...anyone got an idéa whats wrong here?very, very; perhaps too many "very"s!