fracleft(4^n+8^n+1 ight)^-1+frac1nleft(-2^2nln(4^n+8^n+1)-2^3nln(4^n+8^n+1)+ln(2)n imes 2^2n+1+3ln(2)n imes 2^3n-ln(4^n+8^n+1) ight)n^2


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https://math.stackexchange.com/questions/2563344/solving-the-limit-lim-x-rightarrow-infty-sqrt5x5-x4-x
Hint: Let 1/x=himplies h o0 sqrt<5>x^5-x^4=sqrt<5>dfrac1-hh^5=dfracsqrt<5>1-hh Now mix sqrt<5>1-h=yimplies h=1-y^5 lớn have -lim_y o1dfracy-1y^5-1=?
Well, I would multiply top and (missing) bottom by sqrt1+4x+x^2+x. Và then we don't have the somewhat hand-wavy throwing away the -3 as negligible. It is indeed negligible, but developing ...
eginalign sqrt4x^2 + 4 - (2x+2) và = frac(sqrt4x^2 + 4 - (2x+2))(sqrt4x^2 + 4 + (2x+2))sqrt4x^2 + 4 + (2x+2)\ và = frac4x^2 +4 - 4(x+1)^2sqrt4x^2 + 4 + (2x+2) = - frac8xsqrt4x^2 + 4 + (2x+2)\ và = - frac8sqrt4 + 4/x^2 + 2 + 2/x endalign ...
https://math.stackexchange.com/questions/2288362/can-anybody-help-to-find-radius-of-convergence-for-series
Cauchy-Hadamard Formula: sqrtfrac(-3)^n+2^nsqrt<3>n+1 ight=frac1(n+1)^1/3ncdot 3cdotsqrt1+left(-frac23 ight)^n ightxrightarrowfrac11cdot3cdot1=3 ...
https://math.stackexchange.com/questions/799055/calculate-the-limit-of-sqrtn2-3n-n-as-n-rightarrow-infty/799103
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