What is the name of this and is there an easy way to solve it. 1 + (1+2) + (1+2+3) + (1+2+3+...+N)?
399866
There is an easy way to solve it. \n\nThese numbers are known as "pyramidal numbers" as each number in the sequence is equal to the number of blocks in an equilateral pyramid. As a side note, each sum in brackets is known as a "triangular number", as it is equal to the number of blocks in an equilateral triangle (note - a pyramid is a stack of triangles).\n\nMy memory is a little fuzzy on these things, but I believe that the closed-form equation is this:\n\nP(n) = n * (n + 1) * (n + 2) / 6
558121
i=i+2 (i=4)\ni++ (i=5)\ni=5
1160760
what you have is something like\na(b+c)\n\nthe solution is \nab+ac\n\n(x^3)(2x^-2)+(x^3)(4x)\nnow to multiply x^a * x^b you get x^(a+b)\n\n2x^((3+(-2))+4x^(3+1)\n\n2x+4x^4
1099830
27\n\n(+7 -4 +8 -3 +9 -2 +10)
953799
[8+(2*4)]*3 =48 =16*3=30+18=48, just this first expression none of the others
889893
2+7\n3+6\n9+0\n\nThat's it. They all add up to 9... I think that's what the question is asking.
804510
3x^2+6x+5x+10\n(3x+5)(x+2)
952696
n + (n - 5) + (n + 6) \n3n + 1
1157065
(x+5)(2x^2+4x+2)\nx(2x^2+4x+2)+5(2x^2+4x+2)\n2x^3+4x^2+2x+10x^2+20x+10\n2x^3+14x^2+22x+10
920768
One solution is\n0, 2, 4, 6, 8, 10, 12, 1, 3, 5, 7, 9, 11\nBut there is a huge variety of solutions\n\nSorry Chris I did not copy so here is another\n\n0, 11, 5, 2, 9, 3, 1, 4, 10, 7, 12, 6, 8
598513
n + (n+1) + (n+2) = 102\n3n + 3 = 102\n3n = 99\nn = 33\nn+1 = 34\nn+2 = 35\nsecond integer = 34
8373
(([(4+4+4).(4+4)]+4)/4)*(4+4)\n\n(4+(4*4)).([(4+4+4).(4+4)]+4)
859057
2+(n-1)2+1/2(n-1)(n-2)1\n= 2 + 2n - 2 + (1/2)(n^2 - 2n - n + 2)\n= 2n + (1/2)(n^2 - 3n + 2)\n= 2n + (1/2)n^2 - (1/2)(3n) + (1/2)2\n= 2n + (1/2)n^2 - (3/2)n + 1\n= (1/2)n^2 + (1/2)n + 1
527322
1+1-21+30-5\n2-21+30-5\n-19+30-5\n11-5\n6
304206
the clue would be to simplify the equation  to \nlim {x +[-(x+1)+1]}/(x+1)\n x-->0 \nlim [x + 1 -x]/(x+1)\nx-->\nlim (1/(x+1)) =1\nx-->0
503153
(x+7)(x+3)\n(x-11)(x+2)\nforget this one.  its AC factoring though\nthis ones AC too
1178023
a*b is the same thing as adding a b's together. Here are a few examples:\n3*2 = 2+2+2 = 6\n2*3 = 3+3 = 6\n1*6 = 6\n6*1 = 1+1+1+1+1+1 = 6\n4*4 = 4+4+4+4 = 16\n9*9 = 9+9+9+9+9+9+9+9+9 = 81