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what is the sum of the first 57 odd numbers

 Oct 1, 2015

Best Answer 

 #2
avatar+129845 
+10

Note something:

 

1 = 1

 

1 + 3 = 4

 

1 + 3 + 5 = 9

 

1 + 3 + 4 + 9 = 16

 

 

So.....the sum of the first N odd numbers = N^2

 

So   57^2 = 3249

 

 

 

cool cool cool

 Oct 1, 2015
 #1
avatar
0

help him pls

 Oct 1, 2015
 #2
avatar+129845 
+10
Best Answer

Note something:

 

1 = 1

 

1 + 3 = 4

 

1 + 3 + 5 = 9

 

1 + 3 + 4 + 9 = 16

 

 

So.....the sum of the first N odd numbers = N^2

 

So   57^2 = 3249

 

 

 

cool cool cool

CPhill Oct 1, 2015
 #3
avatar+6251 
+5

to elaborate on CPhil's answer.  Consider the sum of the first N odd numbers

 

\(s=\displaystyle{\sum_{k=1}^N}(2k-1) \\ s = 2 \displaystyle{\sum_{k=1}^N}k -\displaystyle{\sum_{k=1}^N}1\\ s=2\dfrac{N(N+1)}{2}-N\\ s=N^2+N-N=N^2\)

 Oct 1, 2015
 #4
avatar+129845 
0

Thanks, Rom   !!!

 

 

cool cool cool

 Oct 1, 2015

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