SOLUTION: a)Determine the differential coefficient with respect to the variable. Y=(x+1)^3 b). find the value of 8+6+4+........+(-32)

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Question 1150587: a)Determine the differential coefficient with respect to the variable.
Y=(x+1)^3
b). find the value of 8+6+4+........+(-32)
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
a)Determine different coefficients with respect to the variable.
Y=(x+1)^3
b). find the value of 8+6+4+........+(-32)
~~~~~~~~~~~~~~ 



(a)  As everybody knows who studied Algebra,  (x+1)^3 = x^3 + 3x^2 + 3x + 1,

     so the coefficients are  1, 3, 3, 1.



(b)  After canceling " + " and " - " terms, you have the sum


         Sum = -2*(5+6+7+8+9+10+11+12+13+14+15+16),    (*)


     and it can be computed in several clicks.  The answer is  -252.



     Also, you may use the formula


        5+6+7+8+9+10+11+12+13+14+15+16 = (1+2+3+4+5+6+ . . . +16) - (1+2+3+4) =  -  = 136-10 = 126,


     and then your sum (*) is  Sum = -2*126 = -252,  giving the same value.


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