can anyone figure this series out?

Question

Consrider a pyramid constructed of stacked spheres ( ex. a pyramid of oranges). The first layer of the pyramid has only one sphere. The second layer( just beneath the first ) has 3 spheres. The third layer has 1 + 2+ 3 = 6 and the Nth layer has 1 + 2 + 3 +....+ N spheres.
Express the number of spheres in the Nth layer as afunction of X?

Answer 1

n(n + 1) / 2

Answer 2

number of spheres in Nth layer is: N(N+1)/2
First layer: N = 1, so number of spheres: 1*(1+1)/2 = 1
Second layer: N = 2, so no. of. spheres: 2*3/2 = 3
3rd layer: N=3 no.of spheres: 3*4/2=6!!!!

Answer 3

layer number
1 1 = 1+0
2 3 = 2+1
3 6 = 3+2+1
: :
N sigma{the sum of}[x=0-->N] (N-x)

Answer 4

N = Sigma (n) where n is in the natural numbers and n goes from 1 to N.