In the expansion of ${(x + y)}^{n}$ , the coefficients of $4 t h$ and $13 t h$ terms are equal, Find $^{'} n^{'}$

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Solution

$(x + y)^{n} = n C_{0} x^{n} y^{0} +^{n} C_{1} x^{n - 1} y + y_{2} x^{n - 2}, . . . .$
$T_{r + 1} =^{n} C_{r} x^{n - r} y^{r}$
$∴ T_{4} =^{n} C_{3} x^{n - 3} y^{3}$
$T_{13} =^{n} C_{12} x^{n - 12} y^{12}$
$∴^{n} C_{3} =^{n} C_{12}$
$∴ n = 3 + 12 = 15$ (Only possibility)
Value of $n = 15$ .

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