If { x } represents the fractional part of x , then { 8 5 200 } is

8 5 200 = 8 ( 5 2 ) 100 = 8 ( 1 + 24 ) 100 = 8 1 + 100 C 1 ⋅ 24 + 100 C 2 ( 24 ) 2 + … . + 100 C 100 ( 24 ) 100 = 8 1 + int eger ⇒ { 8 5 200 } = 8 1

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MathematicsBinomial TheoremProperties of Binomial coefficientsMedium2 min

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If ${x}$ represents the fractional part of $x$ , then ${\frac{5 ^{200}}{8}}$ is

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Solution:

$\frac{5 ^{200}}{8} = \frac{( 5 ^{2} ) ^{100}}{8} = \frac{( 1 + 24 ) ^{100}}{8}$

$= \frac{1 + ^{100} C _{1} \cdot 24 + ^{100} C _{2} ( 24 ) ^{2} + \dots . + ^{100} C _{100} ( 24 ) ^{100}}{8} = \frac{1}{8} + int eger \Rightarrow {\frac{5 ^{200}}{8}} = \frac{1}{8}$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Properties of Binomial coefficients

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