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in Binomial Theorem by (49.9k points)
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In the binomial expansion of (a + b)n , the coefficients of the 4th and 13th terms are equal to each other. Find the value of n.

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To find: the value of n with respect to the binomial expansion of (a + b)n where the coefficients of the 4th and 13th terms are equal to each other

Formula Used: 

A general term, Tr+1 of binomial expansion (x + y)n is given by,

Now, finding the 4th term, we get

T4 = nC3 x an-3 x (b)3

Thus, the coefficient of a 4th term is nC3 

Now, finding the 13th term, we get

T13 = nC12 x an-12 x (b)12

Thus, coefficient of 4th term is nC12 

As the coefficients are equal, we get

n -12 = 3 

n =15 

Thus, value of n is 15

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