# Binary Operations

Calculus Level 5

Define a binary operation $a*b = a+b+ab$ , with $a,b$ are real quantities, where $*$ denotes the symbol of binary operator.

Now this binary operation is associative, commutative and closed under the set of reals.

Denote $S = \displaystyle \lim_{n \to \infty} \left ( 1 * \frac {1}{4} * \frac {1}{9} * \ldots * \frac {1}{n^2} \right )$

Find $\lfloor 100000S \rfloor$.

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