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1,1+2,1+2+3,⋯ \sqrt{1},\quad \sqrt{ 1 + \sqrt{2} },\quad \sqrt{ 1 + \sqrt{2 + \sqrt{3 } } },\quad \cdots 1,1+2,1+2+3,⋯
Consider the above sequence given by an=1+2+3+⋯+n a_n = \sqrt{ 1 + \sqrt{2 + \sqrt{3 + \cdots + \sqrt{n} } } } an=1+2+3+⋯+n.
Does an a_n an converge?
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