Any Help would be awesome, I didn't learn it very well. Thanks.
Compute the sum. \(101^2 - 97^2 + 93^2 - 89^2 + \cdots + 5^2 - 1^2.\)
5304 is the answer
\((101+97)(101-97)+(93+89)(93-89)+...+(5+1)(5-1)=4(101+97+93+89+...+5+1)\)
\(4\times \frac{(1+101)}{2}\times 26\)
\(4\times 51\times 26=5304\)
Thank you! Quick question, where did the 26 come from?
"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
+150 
