中四函數~1題

a) f ( x ) = x^2
f ( x ) - f ( x - 1 )
= x^2 - ( x - 1 )^2
= ( x + x - 1 )( x - x + 1 )
= 2x - 1
bi) f ( 2 ) - f ( 1 ) = 2^2 - 1^2 = 3
ii) f ( 3 ) - f ( 2 ) = 3^2 - 2^2 = 5
iii) f ( 4 ) - f ( 3 ) = 4^2 - 3^2 = 7
iv) f ( 5 ) - f ( 4 ) = 5^2 - 4^2 = 9
c) 3 + 5 + 7 + 9 + ... + 99
= ( 2^2 - 1^2 ) + ( 3^2 - 2^2 ) + ( 4^2 - 3^2 ) + ( 5^2 - 4^2 ) + ... + ( 50^2 - 49^2 )
= - 1^2 + 50^2
= 2499

c) 2499