作业帮求极限limn→∞(2^(1/2)*2^(1/4)*2^(1/8)*...*2^(1/2n))
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求极限limn→∞(2^(1/2)*2^(1/4)*2^(1/8)*...*2^(1/2n))
求极限:limn→∞(2^(1/2)*2^(1/4)*2^(1/8)*...*2^(1/2n))
是求,当n趋近于无穷时,根号2*2开4次方*2开8次方*...*2开2n次方的极限
怎么算得呢?
求极限:limn→∞(2^(1/2)*2^(1/4)*2^(1/8)*...*2^(1/2n))
是求,当n趋近于无穷时,根号2*2开4次方*2开8次方*...*2开2n次方的极限
怎么算得呢?
1/2+1/4+1/8+.1/2^n
=1/2*(1-(1/2)^n)/(1-1/2)
=1-(1/2)^n
limn→∞(2^(1/2)*2^(1/4)*2^(1/8)*...*2^(1/2n))
=lim2^(1/2+1/4+1/8+.+1/2n)
=lim2^(1-(1/2)^n)
=2^(1-0)
=2
我认为最后一项应该是：...*2^(1/2^n)
=1/2*(1-(1/2)^n)/(1-1/2)
=1-(1/2)^n
limn→∞(2^(1/2)*2^(1/4)*2^(1/8)*...*2^(1/2n))
=lim2^(1/2+1/4+1/8+.+1/2n)
=lim2^(1-(1/2)^n)
=2^(1-0)
=2
我认为最后一项应该是：...*2^(1/2^n)
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