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  • The sum of the series <img alt="\binom{10}{0}-\binom{10}{1}+\binom{10}{2}-\binom{10}{3}+\binom{10}{4}+...+\binom{10}{10}" src="/latex-image/?%5Cbinom%7B10%7D%7B0%7D-%5Cbinom%7B10%7D%7B1%7D&amp

The sum of the series \binom{10}{0}-\binom{10}{1}+\binom{10}{2}-\binom{10}{3}+\binom{10}{4}+...+\binom{10}{10} is

 

Option: 1

2


Option: 2

\binom{10}{5}


Option: 3

0


Option: 4

1


Answers (1)

As we learnt

Properties of Binomial Theorem

Sum of Binomial coefficient with alternate signs

C_{0}-C_{1}+C_{2}-C_{3}----=0
 

 

So,  \binom{10}{0}-\binom{10}{1}+\binom{10}{2}-\binom{10}{3}+\binom{10}{4}+...\binom{10}{10}= 0

Posted by

Kshitij

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