Question

(1+2平方分之一)(1+2四次方分之一)````(1+2的2n次方分之一)

Answer 1

(1+（1/2）^2)(1+(1/2)^4)……(1+(1/2)^2n)

=(1-(1/2)^2)(1+（1/2）^2)(1+(1/2)^4)……(1+(1/2)^2n)/(1-(1/2)^2)

=(1-(1/2)^2)(1+（1/2）^2)(1+(1/2)^4)……(1+(1/2)^2n)/(3/4)

(现在用平方差公式（a+b）(a-b)=a^2-b^2)

=(1-(1/2)^4)(1+(1/2)^4)……(1+(1/2)^2n)/(3/4)

……

=(1-(1/2)^2n)(1+(1/2)^2n)/(3/4)

=4*(1-(1/2)^4n)/3