Question

求(1+2分之1)(1+2的平方分之1)(1+2的4次方分之1)(1+2的8次方分之1)+2的15次方分之1 的值

Answer 1

(1+2分之1)(1+2的平方分之1)(1+2的四次方分之)(1+2的八次方分之1)-1

=2*(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)-1

=2*(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)-1

=2*(1-1/2^4)(1+1/2^4)(1+1/2^8)-1

=2*(1-1/2^8)(1+1/2^8)-1

=2(1-1/2^16)-1

=2-1/2^15-1

=1-1/2^15