I don't have all day!
Algebra
Level
3
\[ 1 \# ( 2\# (3\# (4\# \cdots (98 \# 99 )))\cdots ) \]
Let \(\#\) denote a binary operator such that \( \color{red}{a}\# \color{blue}{b} =\color{red}{a}+\color{blue}{b}+\color{red}{a}\color{blue}{b}\). Then what is the value of the expression above?
Notation: \(n!\) denote the factorial of \(n\).
by
Snehan Jayakumar