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Given-the-squence-of-R-x-n-If-n-1-x-k-lt-Find-lim-n-k-1-x-k-n-




Question Number 84367 by bagjamath last updated on 12/Mar/20
      Given the squence of R  (x_n ). If Σ_(n=1) ^∞ x_k <∞,  Find  lim_(n→∞)  ((Σ_(k=1) ^∞ (√x_k ))/( (√n)))=.....
$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Given}\:\mathrm{the}\:\mathrm{squence}\:\mathrm{of}\:\mathbb{R} \\ $$$$\left({x}_{{n}} \right).\:{If}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{x}_{{k}} <\infty, \\ $$$${Find} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\sqrt{{x}_{{k}} }}{\:\sqrt{{n}}}=….. \\ $$$$ \\ $$

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