an=2^n/(2^n+1),求证:a1*a2*a3*a4*a5*.*an>1/(2e)

题目

an=2^n/(2^n+1),求证:a1*a2*a3*a4*a5*.*an>1/(2e)

答案

an=2^n/(2^n+1）=1-1//(2^n+1）大于1-1/n
所以
a1*a2*a3*a4*a5*.*an大于（1-1/n）^n=1/e