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Conjecture a formula for the sum 1/1*3 + 1/3*5 + ... + 1/(2n-1)(2n+1), and prove your...

Conjecture a formula for the sum 1/1*3 + 1/3*5 + ... + 1/(2n-1)(2n+1), and prove your conjecture by using Mathematical Induction.

PLEASE SHOW ALL WORK! PARTICULARLY WITH DEVELOPING FORUMLA!

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