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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)?
x^12 , x^11 ,x^10we want coeffient of x^10which 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 negativesigma of (i(sigma (j)-i)/2 since every hetero combination is counted twiceso 1/2((n(n+1))^2/2^2-(2n+1)(n+1)(n)/6)2717
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