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?
2007-01-14 17:34:00 · 4 answers · asked by JO 2 in Science & Mathematics ➔ Mathematics
X = {N^2 +N} / 2
2007-01-16 05:31:37 · answer #1 · answered by Keith P 7 · 0⤊ 0⤋
OK i got this. this is a summation problem. too bad i can't use sigma notation. but anyway, the sum of the first n digits, starting at 1, for any number of digits, n, is equal to n(n+1)/2
so, 1+2+3 = 3x4/2 = 6
1+2+3+4 = 4x5/2 = 10
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1+2+3+...+n = n(n+1)/2
2007-01-14 17:38:52 · answer #2 · answered by J J 3 · 0⤊ 0⤋
The sum of the integers 1 thru n = n(n+1)/2
2007-01-14 17:41:30 · answer #3 · answered by Northstar 7 · 0⤊ 1⤋
Sn=N(U1+Un)/2
Sn=n(1+n)/2
2007-01-14 17:44:13 · answer #4 · answered by andru 2 · 0⤊ 1⤋