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Question: If ![](https://cdn.pureessence.tech/canvas_289.png?top_left_x=1498&top_left_y=1464&width=300&height=...

If 5n+1+3n−32n5n+2n+32n+3\frac{5^{n + 1} + 3^{n} - 3^{2n}}{5^{n} + 2^{n} + 3^{2n + 3}} is equal to

A

5

B

3

C

1

D

None of these

Answer

None of these

Explanation

Solution

lim⁡n→∞5n+1+3n−32n5n+2n+32n+3\lim _ { n \rightarrow \infty } \frac { 5 ^ { n + 1 } + 3 ^ { n } - 3 ^ { 2 n } } { 5 ^ { n } + 2 ^ { n } + 3 ^ { 2 n + 3 } } lim⁡n→∞5.5n+3n−9n5n+2n+27.9n\lim_{n \rightarrow \infty}\frac{5.5^{n} + 3^{n} - 9^{n}}{5^{n} + 2^{n} + 27.9^{n}}

lim⁡h→∞5.(59)n+(39)n−1(59)n+(29)n+27\lim_{h \rightarrow \infty}\frac{5.\left( \frac{5}{9} \right)^{n} + \left( \frac{3}{9} \right)^{n} - 1}{\left( \frac{5}{9} \right)^{n} + \left( \frac{2}{9} \right)^{n} + 27} = −127\frac{- 1}{27}