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if-a-n-n-4-n-n-1-x-dx-1-x-5-then-1-a-n-is-convergent-or-divergent-2-lim-n-a-n-




Question Number 210969 by universe last updated on 24/Aug/24
    if a_n  = n^4 ∫_n ^(n+1)  ((x dx)/(1+x^5 ))  then      (1) Σa_n  is convergent or divergent??      (2) lim_(n→∞)  a_(n )  = ??
$$\:\:\:\:\mathrm{if}\:\mathrm{a}_{\mathrm{n}} \:=\:\mathrm{n}^{\mathrm{4}} \int_{\mathrm{n}} ^{\mathrm{n}+\mathrm{1}} \:\frac{\mathrm{x}\:\mathrm{dx}}{\mathrm{1}+\mathrm{x}^{\mathrm{5}} }\:\:\mathrm{then} \\ $$$$\:\:\:\:\left(\mathrm{1}\right)\:\Sigma\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{convergent}\:\mathrm{or}\:\mathrm{divergent}?? \\ $$$$\:\:\:\:\left(\mathrm{2}\right)\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{a}_{\mathrm{n}\:} \:=\:?? \\ $$

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