triangle numbers problem, people!!! (you know, 1,3,6,etc) ?

so, here it goes:
theres this crystal pyramid, and on the very top layer there is one crystal.
2nd layer, 3 crystals,
3rd layer, 6.
If this triangle number pattern continues, how many crystals are in the millionth row?
Also, how many crystals in total if you add all previous layers of crystals as well?

What you are describing is the tetrahedral numbers.

The tetrahedral numbers are formed by triangular based pyramids, in which the number of balls in the nth layer is the nth triangular number, which is n(n+1)/2

The total number of balls in a pyramid of n layers is:
n(n+1)(n+2)/6

So in the millionth row there will be 1000000 * 1000001 / 2 = 500000500000 balls.

And in total there will be:
1000000 * 1000001 * 1000002 / 6 = 166667166667000000 balls.

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