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?
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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?](/uploads/image/z/5439532-4-2.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90limn%E2%86%92%E2%88%9E%282%5E%281%2F2%29%2A2%5E%281%2F4%29%2A2%5E%281%2F8%29%2A...%2A2%5E%281%2F2n%29%29%E6%B1%82%E6%9E%81%E9%99%90%3Alimn%E2%86%92%E2%88%9E%282%5E%281%2F2%29%2A2%5E%281%2F4%29%2A2%5E%281%2F8%29%2A...%2A2%5E%281%2F2n%29%29+%E6%98%AF%E6%B1%82%2C%E5%BD%93n%E8%B6%8B%E8%BF%91%E4%BA%8E%E6%97%A0%E7%A9%B7%E6%97%B6%2C%E6%A0%B9%E5%8F%B72%2A2%E5%BC%804%E6%AC%A1%E6%96%B9%2A2%E5%BC%808%E6%AC%A1%E6%96%B9%2A...%2A2%E5%BC%802n%E6%AC%A1%E6%96%B9%E7%9A%84%E6%9E%81%E9%99%90+%E6%80%8E%E4%B9%88%E7%AE%97%E5%BE%97%E5%91%A2%3F)
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))
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))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)
指数项求和 为等比 而且不是2n吧是2的n次方
然后可以求了嘛 就是2-一个趋于0的数就是2了啊
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