Adding consecutive number...

[CrAzY]

That post on Gauss made me think about that adding consecutive number way.

http://forum.valhallalegends.com/phpbbs/index.php?topic=9112.0

Adding 1 + 2 + 3 + ... + 98 + 99 + 100.  The sad thing is knew nothing about it and did the same thing when I was in fourth grade... Guess I'm just not special 

Anyways, bored in math today, I was bored with my calculator and saw some patterns to make that even easier.

Here some formulas for adding consecutive numbers start with 1 -> n.

Note: Both formulas work for even and odds, just you can avoid decimals this way

Formula 1: (I use it for odd ints)
   sum = ((n+1)/2)n
Example: 1+2+3+4+5+6+7+8+9 = 45
          or: (((9)+1)/2)9
              = ((10)/2)9
              = (5)9
              = 45

Formula 2: (I use it for even ints)
   sum=(n/2)n+n/2
Example: 1+2+3+4+5+6+7+8+9+10=55
          or: (10/2)10+10/2
              = (5)10+5
              = 50+5
              = 55

I guess this would only be useful if you used uncomon numbers and large numbers.

I've only really thought about these with positive numbers...  I'm sure someone has seen this before, but hey, watch out Gauss, I'm on a role 

[Yoni]

What grade are you in? Here, they teach this in 10th grade.

http://mathworld.wolfram.com/ArithmeticSeries.html

[Adron]

Summing infinite geometric series is more fun too.

[CrAzY]

Yes, I am in 10th grade.  We aren't exactly doing that though.  Were working with quadratics and imaginary numbers...