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It would be great if someone could help explain this a bit to me, I believe we have to use difference of squares but I dont really know. Thanks!

 

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

 Apr 6, 2021
 #1
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 (a + (2n + 1)d)^2 - (a + (2n)d)^2 + ... + (a + d)^2 - a^2 = (a + (2n + 1) d + (a + 2nd + ... + a + d) + a = n(3a + (n + 2)d).

 Apr 6, 2021
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could you explain?

brazzle  Apr 6, 2021

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