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