+0  
 
+1
79
4
avatar+22 

Any Help would be awesome, I didn't learn it very well. Thanks.

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

 Apr 1, 2021
edited by brazzle  Apr 1, 2021
edited by brazzle  Apr 1, 2021
 #1
avatar+317 
+3

5304 is the answer 

 Apr 1, 2021
 #2
avatar+144 
+1

\((101+97)(101-97)+(93+89)(93-89)+...+(5+1)(5-1)=4(101+97+93+89+...+5+1)\)

\(4\times \frac{(1+101)}{2}\times 26\)

\(4\times 51\times 26=5304\)

.
 Apr 1, 2021
 #3
avatar+22 
+2

Thank you! Quick question, where did the 26 come from?

brazzle  Apr 1, 2021
 #4
avatar+118470 
+2

"26"   is  the  number of  terms  in  ( 101  + 97 + 93  +  ....  + 1)

 

To  see this, note. that

 

(101  - 1)  / 4    +  1   =

 

100/ 4   +  1  =

 

25  +  1   =

 

26

 

cool cool cool

CPhill  Apr 1, 2021

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