已知y1=2a(a不等于0),y2=2/y1,y3=2/y2,y4=2/y3,...,y2008=2/y2007,求y1*y2008的值

Question

已知y1=2a(a不等于0),y2 = 2/y1,y3 = 2/y2,y4 = 2/y3,...,y2008 = 2/y2007,求y1 * y2008的值

Answer 1

y1*y2=y1*2/y1=2
y3*y4=y3*2/y3=2
...
y2007*y2008=y2007*2/y2007=2
y1*y2*...*y2008=2^1004
y2*y3=y2*2/y2=2
y4*y5=y4*2/y4=2
...
y2006*y2007=2
y2*y3*...*y2007=2^1003
y1*y2008=(y1*y2*...*y2008)/(y2*y3*...*y2007)=2^1004/2^1003=2
y1=2a,y2=1/a,y3=2a,y4=1/a,...y2007=2a,y2008=1/a
y1*y2008=2