+579 So, I need to know why the powers of eleven are the numbers of the Pascal Triangle
11^0=1
11^1=11 (duh)
11^2=121
11^3=1331
11^4=14641
and so on...
why is this?
+128408 Not an expert here....but notice that, working backwards
110 = 1
111 = (10 + 1)1 = C(1,0)* 10 + C(1,1) * 1 = 10 + 1 = 11
112 =
(10 + 1)2 = C(2, 0) * 102 + C(2, 1) * 10 + C(2, 2) * 1 =
100 + 2*10 + 1 =
121
113 =
(10 + 1)3 =
C(3, 0) 103 + C(3,1)* 102 + C(3,2) * 10 + C(3,3) * 1 =
103 + 3 * 102 + 3 * 10 + 1 =
1000 + 300 + 30 + 1 =
1331
etc.........
