Binary Operations

Calculus Level 5

Define a binary operation ab=a+b+ab a*b = a+b+ab , with a,b 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=limn(114191n2)S = \displaystyle \lim_{n \to \infty} \left ( 1 * \frac {1}{4} * \frac {1}{9} * \ldots * \frac {1}{n^2} \right )

Find 100000S \lfloor 100000S \rfloor .

This is original. Check out my Set
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