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What is the coefficient of x^10 in the expansion of (x+1)(x+2)(x+3)(x+4)(x+5)(x+6)(x+7)(x+8)(x+9)(x+10)(x+11)(x+12)?

What is the coefficient of x^10 in the expansion of (x+1)(x+2)(x+3)(x+4)(x+5)(x+6)(x+7)(x+8)(x+9)(x+10)(x+11)(x+12)?

Grade:11

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
8 years ago
x^12 , x^11 ,x^10

we want coeffient of x^10

which is sum of all possible combination 1*2+2*3+3*4+4*5 ....

-(sigma of i*j where i not equal to j from 1 to 12) since roots are all negative

sigma of (i(sigma (j)-i)/2 since every hetero combination is counted twice

so 1/2((n(n+1))^2/2^2-(2n+1)(n+1)(n)/6)

2717



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