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please give thorough explanations, i am confused about how to solve this properly... I thought using a^2 - b^2 = (a - b)(a + b) would work, but I don't think it is the most efficient way.

 

(a) Compute the sum:

                                              \(101^2 - 97^2 + 93^2 - 89^2 + \cdots + 5^2 - 1^2.\)

(b) Compute the sum: 

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

 Jun 24, 2020
 #1
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This has been posted before.  Try searching for it.

 Jun 24, 2020
 #2
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someone has posted it before, but there was no clear response. I was hoping for a very clear and thorough explanation.

Guest Jun 24, 2020
 #3
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Using difference of squares is the most efficient way. I don't know how to do part (b), but I can certainly explain part (a).

 

 Jun 24, 2020
 #4
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(b) - See Alan's answer here:  https://web2.0calc.com/members/alan/?answerpage=751

 

(a) - sum_(n=1)^26 (-1)^(n + 1) (105 - 4 n)^2 = 5304

 Jun 24, 2020

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