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1#(2#(3#(4#⋯(98#99)))⋯ ) 1 \# ( 2\# (3\# (4\# \cdots (98 \# 99 )))\cdots ) 1#(2#(3#(4#⋯(98#99)))⋯)
Let #\## denote a binary operator such that a#b=a+b+ab \color{#D61F06}{a}\# \color{#3D99F6}{b} =\color{#D61F06}{a}+\color{#3D99F6}{b}+\color{#D61F06}{a}\color{#3D99F6}{b}a#b=a+b+ab. Then what is the value of the expression above?
Notation: n!n!n! denote the factorial of nnn.
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