i just work with it some more and found a pattern...
1. 1^2-2^2+3^2-4^2+5^2
just focus on the last number, in this case, 5^2.
if the last number is odd, add 1 to the number, divide the result by 2, and multiply by the original number. so the last number is 5, add 1 is 6, divide 6 by 2 is 3, and multiply 3 by the original last number, 5.
the answer is 15, and if the last number is odd, it's always positive.
if the last number is even, still, focus on the last number, divide it by 2, use the result and multiply by the original number plus 1.
so...if....1^2-2^2+3^2-4^2+5^2+6^2
6 divided by 2 is 3, use 3 times (6+1), which is 21
the answer is -21, when the last number is even, it's always negative
i am pretty sure that's how it works...i've tried many times and it worked, plz tell me if i am wrong
Very good. You are learning how to develop your own formulas. That was very nice and yes, you are correct, the formula for that is n(n+1)/2. You just need to watch your negative signs.
Notice, everything is going to cancel out except for the last terms. We will be left with n + (n-1). If we took this all the way from n^2 down to 1^2, we will be left with:
n + (n-1) + (n-2) + ... + 3 + 2 + 1 which is n(n+1)/2 or a triangular number.
