# JEE Main 2016 (22)

Algebra Level 5

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

The equation above holds true for constants $$A_1, A_2, \ldots , A_{25}$$. Find the sum of digits of the number $$A_{24}$$.

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

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