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avatar+732 

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

 

Thanks in advance to whoever helps! I'm very grateful! :)

 May 19, 2020
 #1
avatar+111455 
+3

Note  that we  can write this as

 

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

 

(101 - 97) (101 + 97)  +  ( 93 - 89) (93 + 89)  +  ( 85 - 81)(85 + 81) + (77 - 73) (77 + 73) + ..+ (5 - 1) (5 + 1)  =

 

4   [ 198   +  182  +  166   + 150 +   ....+  6 ]  

 

The  number  of terms  inside  the btackets  =   [198 - 6] / 16  + 1  =  12 + 1  =  13

 

So.....using  the sum of an arithmetic series.....the sum is

 

4 *  [ 198 + 6]  / (13/2)=

 

26  [ 204]  =

 

5304

 

 

cool cool cool

 May 20, 2020
 #2
avatar+732 
+1

thank you so much for the clear and concise answer, I understand how to solve it now!!! I'm really thankful that there are people like you on the forum :)))

lokiisnotdead  May 20, 2020
 #3
avatar+111455 
0

OK, THX....I appreciate  that    !!!!!

 

 

cool cool cool

CPhill  May 20, 2020

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