OK I GOT IT!! i was trying to figure out pattern instead of doing the problem, cuz it still helps my math in college and it helps u understand WTF is going on.
question 1.
equation ((n)(n+1))/2 is how many things there are in a series.
for example in ur case
1
2 2
3 3 3
4 4 4 4
5 5 5 5 5
etc is your series correct?
so if u do this
1 1 2 3 4 5
2 2 2 3 4 5
3 3 3 3 4 5
4 4 4 4 4 5
5 5 5 5 5 5
wat i did here was stack another triangle
1
2 2
etc
sideways on top of the first triangle
thus u get 6 units lengthwise and 5 widthwise
total 30
so because we ended at 5, we set n=5
thus 6x5 = (n+1)(n)
and because were dealing with only half of that.
((n+1)(n))/2
alrite
so u keep chucking in higher numbers cuz plugging in 5 only gives u 15 -- keep plugging in numbers for N and as soon u pass 1,000,000 -- thats the number u keep. if ur (n-1) is smaller than 1,000,000 and ur (n) is bigger than the million. that (n) is what the millionth number is.
enjoy. ask me more if u like. i gots hella time