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  • What is the sum of coefficients <img alt="\binom{5}{0}+\binom{5}{2}+\binom{5}{4}?" src="https://learn.careers360.com/latex-image/?%5Cbinom%7B5%7D%7B0%7D&plus;%5Cbinom%7B5%7D%7B2%7D&plu

What is the sum of coefficients \binom{5}{0}+\binom{5}{2}+\binom{5}{4}?

Option: 1

2^5


Option: 2

2^4


Option: 3

2^6


Option: 4

2


Answers (1)

best_answer

As we learnt

 

Properties of Binomial Theorem -

 

Sum of the binomial coefficients of the odd term is equal to sum of the binomial coefficients of even term and each is equal to 2^{n-1}.
 

- wherein

c_{0}+c_{2}+c_{4}----

= c_{1}+c_{3}+c_{5}----

= 2^{n-1}

 

 

 \binom{5}{0}+\binom{5}{2}+\binom{5}{4}=\binom{5}{1}+\binom{5}{3}+\binom{5}{5}= \frac{2^5}{2}= 2^{4}

Posted by

avinash.dongre

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