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Question Number 57850 by Mikael_Marshall last updated on 13/Apr/19

$$\underset{n\to \mathrm{\infty }}{lim}\frac{8^n}{2^{n+1}+3^{n+2}}$$

Answered by tanmay.chaudhury50@gmail.com last updated on 13/Apr/19

$$\underset{n\to \mathrm{\infty }}{\lim }\frac{8^n}{2\times 2^n+3^2\times 3^n}$$$$8^n>3^n>2^n$$$$\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{2\times {\left(\frac{2}{8}\right)}^n+9\times {\left(\frac{3}{8}\right)}^n}$$$$=\frac{1}{2\times 0+9\times 0}$$$$sowhenn\to \mathrm{\infty }givenlimit\to \mathrm{\infty }$$$$$$

Commented by Mikael_Marshall last updated on 13/Apr/19

$$thanksSir.$$

Commented by tanmay.chaudhury50@gmail.com last updated on 13/Apr/19

$$mostwelcome$$

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