+738 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! :)
+129852 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
+738 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 :)))
