Coefficient

Probability Level 4

Find the coefficient of $x^{15}$ in the expansion of $(1-x)(1-2x)(1-4x)(1-8x)\cdots(1-32768x)$

2^{105} - 2^{121}

2^{121} - 2^{105}

2^{120} - 2^{104}

2^{110} - 2^{108}

1 solution

Mohit Gupta
Mar 26, 2016

@Vaibhav Gupta A small suggestion you can modify the options to make this problem reasonable and hardet.....since we know there are 15 brackets to be multiplied therefore $-2^{n}$ would be multiplied from n=1 to 15,therefore making obvious that product will be Negative .

Now consider your options only last option would result in negative number others are all positive as clearly visible by observation.....so the problem is greatly reduced in applying concept.....Isn't it??

Coefficient

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