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The expression^{n}C_{r+1}+^{n}C_{r-1}+2\times \; ^{n}C_{r} \; equals

Option: 1

^{n+2}C_{r+1}\;


Option: 2

\; \; ^{n+1}C_{r}\;


Option: 3

\; ^{n+1}C_{r+1}\;


Option: 4

\; \; ^{n+2}C_{r}\;


Answers (1)

best_answer

As we have learned

Properties of Binomial Theorem -

\dpi{120} ^{n}C_{r}+^{n}C_{r-1}= ^{n+1}C_{r}

 

Now,

^{n}C_{r+1}+ ^nC_{r-1} +2\times ^nC_{r}

(^{n}C_{r+1}+ ^nC_{r}) +(^nC_{r-1} + ^nC_{r})

(^{n+1}C_{r+1}) +(^{n+1}C_{r} )

(^{n+2}C_{r+1})

Posted by

Pankaj

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