Happy birthday Adarsh Kumar!

Probability Level 4

( 1 − x ) ( 1 + 2 x ) ( 1 − 3 x ) ⋯ ( 1 + 14 x ) ( 1 − 15 x ) \large (1 - x)(1 + 2x)(1 - 3x)\cdots(1 + 14x)(1 - 15x)

Find the coefficient of x 2 x^2 in the expansion above.


The answer is -588.

Parth Lohomi by Parth Lohomi , 20, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Aamir Ibrahim
May 18, 2015

Since the x^2 term can be formed by multiplying the x terms in any of the two factors, the coefficient will be given by

-1(2-3+4-5+6-7+.......14-15) + 2(-3+4-5+6-7+.......+14-15)-3(4-5+6-7+......+14-15)+....................-13(14-15)+14(-15)

= -1(-7) +2(-9) -3(-6)+4(-10)-...............-13(-1)+14(-15) =122-710 = -588

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...