设函数f(x)=1/x,数列an满足：a1=a不等于0,且对于任意的正整数n都有an+1=f(an^2),则a1*a2…*a10=

题目

设函数f(x)=1/x,数列an满足：a1=a不等于0,且对于任意的正整数n都有an+1=f(an^2),则a1*a2…*a10=

答案

a1=a
a2=1/a^2
a3=a^4
a4=1/a^8
……
a1*a2…*a10=1/a(1+2^2+2^4+2^6+2^8)=1/a^341