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  • Solve this problem - If , then k equals : - Binomial theorem and its simple applications - JEE Main

 

If , \sum_{i=1}^{20}\left ( \frac{^{20}C_{i-1}}{^{20}C_{i}+^{20}C_{i-1}} \right )^{3}=\frac{k}{21}then k equals :

  • Option 1)

     

    400

  • Option 2)

     

    50

  • Option 3)

     

    200

  • Option 4)

     

    100

Answers (1)

best_answer

 

Properties of Binomial Theorem -

\dpi{120} \frac{^{n}c_{r-1}}{^{n}c_{r}}= \frac{r}{n-r+1} and

-

 

\sum_{i=1}^{20} (\frac{^{20}C_{i-1}}{^{20}C_{i} +^{20}C_{i-1}} )^{3} = \frac{K}{21}

From the concept

\Rightarrow \sum_{i=1}^{20} (\frac{^{20}C_{i-1}}{^{21}C_{i} } )^{3} = \frac{K}{21}

\Rightarrow \sum_{i=1}^{20} (\frac{1}{21 } )^{3} = \frac{K}{21}

\Rightarrow \frac{1}{21^{3} } . \left [ \frac{20 \times 21}{2} \right ]^{2}= \frac{K}{21}

K = 100

 

 


Option 1)

 

400

Option 2)

 

50

Option 3)

 

200

Option 4)

 

100
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