Question

问大家一道计算题 ,1:计算,(1+2分之一)(1+2的平方分之一)(1+2的四次方分之一)(1+2的8次方分之一)+2

Answer 1

原式=(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)/(1-1/2)+1/2^15

=[1^2-(1/2)^2](1+1/2^2)(1+1/2^4)(1+1/2^8)/(1/2)+1/2^15

=2(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15

=2*(1-1/2^4)(1+1/2^4)(1+1/2^8)+1/2^15

=2*(1-1/2^8)(1+1/2^8)+1/2^15

=2*(1-1/2^16)+1/2^15

=2-2/2^16+1/2^15

=2-1/2^15+1/2^15

=2