INTEGER \[+\frac{1}{15}\] Hence, the FRACTIONAL part of \[\frac{{{2}^{4n}}}{15}\]is \[\frac{1}{15}\]

"> INTEGER \[+\frac{1}{15}\] Hence, the FRACTIONAL part of \[\frac{{{2}^{4n}}}{15}\]is \[\frac{1}{15}\]

">
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The fractional part of \[{{2}^{4n}}/15\]is \[(n\in N)\]

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) 11 months ago

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[a] \[{{\left( \frac{1}{x} \right)}^{r}}{{=}^{m}}{{C}_{r}}{{x}^{2m-3r}}=\frac{{{(15+1)}^{n}}}{15}\] \[=\frac{{{(}^{n}}{{C}_{0}}{{15}^{n}}{{+}^{n}}{{C}_{1}}{{15}^{n-1}}+...{{+}^{n}}{{C}_{n-1}}15{{+}^{n}}{{C}_{n}})}{15}\] = INTEGER \[+\frac{1}{15}\] Hence, the FRACTIONAL part of \[\frac{{{2}^{4n}}}{15}\]is \[\frac{1}{15}\]

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Posted on 11 Aug 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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