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  • Find the limit of  <img alt="\mathrm{\frac{3^{2 n+1}+2^{3 n+1}}{7^{n+2}+9^n}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cfrac%7B3%5E%7B2%20n&plus;1%7D&plus;2%

Find the limit of  \mathrm{\frac{3^{2 n+1}+2^{3 n+1}}{7^{n+2}+9^n}}

Option: 1

0


Option: 2

3


Option: 3

4


Option: 4

1


Answers (1)

best_answer

We rewrite the sequence as

                                   \mathrm{ \lim _{n \rightarrow \infty} \frac{3 \cdot 9^n+2 \cdot 8^n}{49 \cdot 7^n+9^n} }

and then divide by \mathrm{9^n :}

                                    \mathrm{ \lim _{n \rightarrow \infty} \frac{3+2(8 / 9)^n}{49(7 / 9)^n+1} }

Now \mathrm{(7 / 9)^n} and \mathrm{(8 / 9)^n} tend to zero, and the limit thus reduces to

                                    \mathrm{ \frac{3}{1}=\frac{3 \cdot 9^n}{9^n}=\frac{3^{2 n+1}}{9^n}=3 }

Posted by

Ritika Harsh

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