what will be the cofficient of x^16 & x^17 in the expension (x+1)(x+2)(x+3)(x+4)..........(x+18)???

Asked by Piyush Gupta | 20th Oct, 2010, 12:00: AM

Expert Answer:

The coefficient of x17  in the expression (x+1)(x+2)(x+3)(x+4)..........(x+18) will be given by
Sum of 1,2,3.................18
So, coefficient of x17  = 1+2+3+.....18
Sum of n natural numbers is given by
coefficient of x17  = 171
 
Coefficent of x16 = sum of product of roots taken two at a time
= (1.18 + 1.17 + 1.16..........1.2)+(2.18+2.17..........2.3) +  ............+ 17(18)
= 18(1+2+.....17)+17(1+2+3........16)+16(1+2+3.....15)+..............+.2(1)
Solve the above expression by using the formula for sum of n natural numbers to get the value of coefficient of x16
 
 

Answered by  | 22nd Oct, 2010, 12:25: PM

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