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Exercise:
Calcola _n^inftyfrac-nn^-n

Solution:
Possiamo riscrivere frac-nn^-nfracn++fracn--fracn. Riscriviamo fracn as fracn da cui * S&:_nge leftfracn--fracn+fracn+right _nge _^ x^n-left-x+x^rightmathrm dx _^fracx-x^+x^-x^mathrm dx. * Di conseguenza * S_^frac+x+x+x^mathrm dxfrac_^frac+x+x+x^mathrm dx+frac_^fracmathrm dx+x+x^. & fracln+x+x^+fracsqrt arctanleftfracx+sqrtright Bigg|_^ fracln+fracpi sqrt. *
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Exercise:
Calcola _n^inftyfrac-nn^-n

Solution:
Possiamo riscrivere frac-nn^-nfracn++fracn--fracn. Riscriviamo fracn as fracn da cui * S&:_nge leftfracn--fracn+fracn+right _nge _^ x^n-left-x+x^rightmathrm dx _^fracx-x^+x^-x^mathrm dx. * Di conseguenza * S_^frac+x+x+x^mathrm dxfrac_^frac+x+x+x^mathrm dx+frac_^fracmathrm dx+x+x^. & fracln+x+x^+fracsqrt arctanleftfracx+sqrtright Bigg|_^ fracln+fracpi sqrt. *
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Extra, Successioni e serie
Difficulty
(3, default)
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0 (default)
Language
ITA (Italiano)
Type
Calculative / Quantity
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