S=1+2 negative first power +2 negative second power +2 negative third power ++2 negative 2005 power, how much is S equal?

S=1+2 negative first power +2 negative second power +2 negative third power ++2 negative 2005 power, how much is S equal?

A summation formula using a series of proportional numbers.
S=[1-(1/2)^2006]/[1-(1/2)]
=2[1-(1/2)^2006]
=2-1/2^2005

If the rational number a is equal to its reciprocal and the rational number b is equal to its opposite, then a 1998+b1998=() A.0 B.1 C.-1 D.2

The rational number a is equal to its reciprocal, i.e. a=1
A⇒ a2=1, so a =±1, so a 1998=1,
The rational number b is equal to its opposite number, then b =-b, i.e.2b =0⇒ b =0, so b1998=0,
So a1998+b1998=1+0=1
Therefore, select B