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

 Jan 23, 2020
 #1
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Please help me

 Jan 23, 2020
 #2
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Halpp

 Jan 23, 2020
 #3
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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).

 Jan 23, 2020
 #4
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I need the explanation to help please

 Jan 31, 2020

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