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

问题描述:

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

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