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avatar+59 

a) Compute the sum of 

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

 

b) Compute the sum of 

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

 

An explanation might be helpful too. Thanks!

 Apr 1, 2021
 #1
avatar+1231 
+1

The key to question A is that (a+b)(a-b) = a^2 - b^2

So we can split the question into parts. 

(101+97)(4) + (93+89)(4)...(5+1)(4). 

Which is also equal to 

4(101+97+93+89...+5+1)

4*102*26/2 = 5304. 

 

Try using the concept of (a+b)(a-b) = a^2 - b^2 for the second problem. :))

 

=^._.^=

 Apr 1, 2021

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