证明lim(1+1/2)×(1+1/2²)×……×(1+1/2^2^(n-1))n→∞存在如题...注意是证明存在
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证明lim(1+1/2)×(1+1/2²)×……×(1+1/2^2^(n-1))n→∞存在如题...注意是证明存在
证明lim(1+1/2)×(1+1/2²)×……×(1+1/2^2^(n-1))n→∞存在
如题...注意是证明存在
证明lim(1+1/2)×(1+1/2²)×……×(1+1/2^2^(n-1))n→∞存在如题...注意是证明存在
证明:∵ lim(n->∞)[(1+1/2)(1+1/2²).(1+1/2^2^(n-1))]
=lim(n->∞)[(1-1/2)(1+1/2)(1+1/2²).(1+1/2^2^(n-1))/(1-1/2)]
=lim(n->∞)[(1-1/2^2^n)/(1-1/2)]
=(1-0)/(1-1/2)
=2
∴lim(n->∞)[(1+1/2)(1+1/2²).(1+1/2^2^(n-1))]存在.