SOLUTION: Boxes are stored in a warehouse. The stack is four boxes wide and 20 boxes long at the bottom. Each layer is one box shorter than the previous layer but the same width. How many bo

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Question 472127: Boxes are stored in a warehouse. The stack is four boxes wide and 20 boxes long at the bottom. Each layer is one box shorter than the previous layer but the same width. How many boxes are there if the top layer is four boxes long? Write an equation with summation notation to find the total number of boxes. If you solve this question without using summation notation, you may not get full marks.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the sum of digits 1 through n = +%281%2F2%29%2An%2A%28n%2B1%29+
The sum of the boxes looks like:
+4%2A20+%2B+4%2A19+%2B+4%2A18+ . . . to +4%2A4+
If the top layer was +4%2A1, the answer would be
Sum = +4%2A%281%2F2%29%2A20%2A21+
But I want to subtract +4%2A3+%2B+4%2A2+%2B+4%2A1+ from this, so
Sum = +2%2A20%2A21+-+4%2A%281%2F2%29%2A3%2A4+
Sum = +2%2A20%2A21+-+2%2A3%2A4+
Sum = +840+-+24+
Sum = +816+
In summation notation, this would look like:
4 x 1/2 x Sum, n from 1 to 20 of n
minus 4 x 1/2 x Sum, n from 1 to 3 of n