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(a) Compute the sum \(101^2 - 97^2 + 93^2 - 89^2 + \cdots + 5^2 - 1^2.\)
(b) Compute the sum \((a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + \cdots + (a+d)^2 - a^2.\)

 Aug 20, 2020
 #1
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(a) 101^2 - 97^2 + 93^2 - 89^2 + ... + 5^2 - 1^2 = 101 + 97 + 93 + 89 + ... + 5 + 1 = 1326.

 

(b) (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).

 Aug 20, 2020
 #2
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a -  sum_(n=1)^26 (-1)^(n + 1) (105 - 4 n)^2 = 5304

 Aug 20, 2020
 #3
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b - See detailed step by step answer by "heureka" in the middle of page 531 here:  https://web2.0calc.com/members/heureka/?answerpage=531

 Aug 20, 2020

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