Question

括号1+1/2乘括号1+2的二次方分之1×括号1+2的四次方分之1×括号1+2的八次方

括号1+1/2乘括号1+2的二次方分之1×括号1+2的四次方分之1×括号1+2的八次方分

Answer 1

（1+1/2）×（1+1/2的2次方）×（1+1/2的4次方）×（1+1/2的8次方）
=（1-1/2）（1+1/2）×（1+1/2的2次方）×（1+1/2的4次方）×（1+1/2的8次方）/（1-1/2）
=（1-1/2的2次方）×（1+1/2的2次方）×（1+1/2的4次方）×（1+1/2的8次方）×2
=（1-1/2的4次方）×（1+1/2的4次方）×（1+1/2的8次方）×2
=（1-1/2的8次方）×（1+1/2的8次方）×2
=（1-1/2的16次方）×2
=2-1/2的15次方

Answer 2

=(1-1/2)(1+1/2)(1+1/2²)(1+1/2的4方)(1+1/2的8方)÷(1-1/2)
=(1-1/2²)(1+1/2²)(1+1/2的4方)(1+1/2的8方)ⅹ2
=2(1-1/2的16方)
=2-1/2的17方

Answer 3

(1+½)(1+½²)(1+½⁴)(1+½⁸)
=2·(1-½)(1+½)(1+½²)(1+½⁴)(1+½⁸)
=2·(1-½²)(1+½²)(1+½⁴)(1+½⁸)
=2·(1-½⁴)(1+½⁴)(1+½⁸)
=2·(1-½⁸)(1+½⁸)
=2·(1-½¹⁶)
=2-½¹⁵
=65535/32768