+69 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!
+2407 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. :))
=^._.^=
