Which sequence do you get when you start to add the All 1’s sequence up? What sequence do you get when you add the All 1’s sequence up and down?
By imagining a large version of your picture, or drawing it partially, as needed, can you see what will be tha value of 1 + 2 + 3 + … + 99 + 100 + 99 + … + 3 + 2 + 1?
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Sum of 1 + 2 + 3 + … + 99 + 100 + 99 + … + 3 + 2 + 1:
This sequence will form a large square with side length 100, resulting in a sum of 100 × 100 = 10,000. This pattern holds because the symmetrical arrangement builds a square with the largest number (100) as its side length.
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