JEE Main 2016 (22)

Algebra Level 5

25!x(x+1)(x+2)(x+25)=i=025Aix+i\dfrac{25!}{x(x+1)(x+2)\cdots(x+25)}=\sum_{i=0}^{25}\dfrac{A_{i}}{x+i}

The equation above holds true for constants A1,A2,,A25A_1, A_2, \ldots , A_{25} . Find the sum of digits of the number A24A_{24} .

Notation:
!! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .


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