Question

a) ( 1 - 2 )² + ( x -4 )³ + ( 4 - 5 )⁴ + ...+ ( 99 - 100 )⁹⁹

b) 1² - 2² + 3² - 4² + 5² - 6² + ...+ 99² - 100²

Answer 1

a) S=(1-2)^2+(3-4)^3+......+(99-100)^99

=(-1)^2+(-1)^3+......+(-1)^99

=1+(-1)+....+(-1)

=[1+(-1)]+[1+(-1)]+.......+[1+(-1)]

=0+0+.....+0=0

Answer 2

1^2-2^2+3^2-4^2+.......+99^2-100^2

=(1+2)(-1)+(3+4)(-1)+......+(99+100)(-1)

=(-1)(1+2+3+4+......+99+100)=(-1).101.100:2=-5050