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In the binomial expansion of (a+b)^n , c...

In the binomial expansion of `(a+b)^n` , coefficients of the fourth and thirteenth terms are equal to each other. Find `n` .

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In `(a + b)^n` general term is
` t_(r + 1) = n_(C_r) a^(n - r) b^r`
We are given that their coefficients are equal
`t_4=t_(13)`
` n_(C_3) = n_(C_(12)) `
=`n = 12 + 3 = 15`
as ` [n_(C_x) = n_(C_y) ⇒ x = y (or) x + y = n]`
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