limn→∞5n+1+3n−22n5n+2n+32n+3=

limn→∞5.5n+3n−4n5n+2n+27.9n=limn→∞5.59n+39n−49n59n+29n+27=0+0−00+0+27=0

limn→∞5n+1+3n−22n5n+2n+32n+3=

limn→∞5.5n+3n−4n5n+2n+27.9n=limn→∞5.59n+39n−49n59n+29n+27=0+0−00+0+27=0

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$\lim_{n \to \infty} \frac{5^{n + 1} + 3^{n} - 2^{2 n}}{5^{n} + 2^{n} + 3^{2 n + 3}} =$

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answer is D.

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Detailed Solution

$\lim_{n \to \infty} \frac{{5.5}^{n} + 3^{n} - 4^{n}}{5^{n} + 2^{n} + {27.9}^{n}} = \lim_{n \to \infty} \frac{5. {(\frac{5}{9})}^{n} + {(\frac{3}{9})}^{n} - {(\frac{4}{9})}^{n}}{{(\frac{5}{9})}^{n} + {(\frac{2}{9})}^{n} + 27} = \frac{0 + 0 - 0}{0 + 0 + 27} = 0$