+0  
 
+1
304
4
avatar+578 

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?

 #1
avatar+92808 
+2

Not an expert here....but notice that, working backwards

 

11  =  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.........

 

 

cool cool cool

CPhill  Dec 1, 2017
 #2
avatar+578 
+1

I am thoroughly baffled

 #3
avatar+578 
+2

NO DONT MARK THIS AS ANSWERED I DONT UNDERSTAND IT YET

 #4
avatar+94126 
+2
Melody  Dec 2, 2017

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