the coefficient of x⁴⁹ in the polynomial {x-(C_1/C0)}{x-2²(C_2/C1)}{x-3²(C_3/C2)}.....{x-50²(C_50/C49) is........?

ans in the form of summation will do and give the steps followed.

Dear nishant

let the polinomial is

 x50 + A₄₉x⁴⁹ +A₄₈ x⁴⁸...........+ A1 x +A0 =0

 whose roots are  (C_1/C0) ,2²(C_2/C1) ,3²(C_3/C2) ......50²(C_50/C49)

so   sum of roots = -A₄₉

      A₄₉ =  -[ (C_1/C0) + 2²(C_2/C1)+  3²(C_3/C2) ......+50²(C_50/C49)]

             =     r :1 to 50  ∑-r²(C_r/C _r-1)

             =     r :1 to 50  ∑r²-51r

             =   r :1 to 50  ∑r²     -   r :1 to 50   ∑51r

             =  22100

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