Question

In the Binomial expansion of (a + b)^n the coefficient of 4th and 13th terms are equal to each other. find n?

Answer 1

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♦ Binomial Theorem ♦

 ◘ Recall : (r)th binomial coefficient = C(n,r-1)

According to question :-
  • Coeff. [ 4th Term ] = Coeff. [ 13th term ]
 => C( n , 4 - 1 ) = C( n , 13 - 1 ) 
 => C( n , 3 ) = C( n , 12 )

 ◘ Recall : C( n , r ) = C( n , n - r )
 => r = 3 ; n - r = 12
 => n = 15 
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► Hence, the required binomial expansion is : ( a + b )¹⁵ also given by :
$\sum_{n=0}^{15} (^{ \ 15 \ }_{ \ n \ })a^{15-n}b^n$

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Hope this helps 

Answer 2

Answer:

Please check the attachment that I have posted.

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