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h v Grade: 12
        

dear sir,


solve for n;(2n+1)C1 here is:out of 2n+1 objects, 1 object selected...and not (2n+1)*C1


(2n+1)C1 + (2n+1)C2 + (2n+1)C3 +....+(2n+1)Cn = 63


[answer ; n=3]

7 years ago

Answers : (2)

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
										

Dear H V,


Ans:- Let us consider the expansion (1+X)^(2n+1)


(1+X)^(2n+1)=(2n+1)C0+(2n+1)C1 X +(2N+1)C2 X²+............+(2N+1)C2N X^2N+(2N+1)C(2N+1)X^2N+1................1


Now we know that NCr=NC(N-r)


(2N+1)C1=(2n+1)C2N


(2N+1)C2=(2N+1)C(2N-1)       


Again ,


(2N+1)CN=(2N+1)C(N+1) etc


Hence from these relations we get,(Putting X=1 in eq 1)


2^(2N+1)=(2N+1)C0+2K+(2N+1)C(2N+1)


where K=(2N+1)C1+(2N+1)C2+..............(2N+1)C(2N+1)=63(given)


2^(2N+1)=1+1+126=128


4^N=64=4³


Hence N=3(Ans) 


 


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All the best H V !!!


 



Regards,


Askiitians Experts
Soumyajit Das IIT Kharagpur

7 years ago
h v
33 Points
										

can anyone give the answer please?

6 years ago
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