Find the ratio of the coefficient of x15 to the term independent of x in the expansion of .

To Find: the ratio of the coefficient of x15 to the term independent of x


Formula :


Here, a=x2, and n=15


We have a formula,







To get coefficient of x15 we must have,


(x)30-3r = x15


• 30 - 3r = 15


• 3r = 15


• r = 5


Therefore, coefficient of x15


Now, to get coefficient of term independent of xthat is coefficient of x0 we must have,


(x)30-3r = x0


• 30 - 3r = 0


• 3r = 30


• r = 10


Therefore, coefficient of x0


But ……….


Therefore, the coefficient of x0


Therefore,





Hence, coefficient of x15 : coefficient of x0 = 1:32


Conclusion : The ratio of coefficient of x15 to coefficient of x0 = 1:32


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