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Compute the sum (a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + ... + (a+d)^2 - a^2

 

I am confused, how can I figure out the number of terms from here? I know that it decreases by d with each term. But I don't know that number of terms. How does 2n-1 become 0?

 Mar 24, 2020
edited by Guest  Mar 24, 2020
 #1
avatar+21017 
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Notice that the coefficient of d decreases:

    2n + 1,  2n,  2n - 1,  2n - 2,  ...   1

 

The way that the coefficient can become one if the coefficient is   '2n - '

so that  '2n -

If  'something' is '2n - 1'  then  2n - (2n- 1)  =  2n - 2n + 1  =  1. 

 Mar 24, 2020
 #2
avatar+1970 
+1

Nice, Geno!

CalTheGreat  Mar 24, 2020
edited by CalTheGreat  Mar 24, 2020
 #3
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0

ok I get it now thank you!

 Mar 25, 2020

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