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Provide complete solutions Answer the following in a separate sheet of paper. Show your solution I. Mathematical Induction and Binomial Theorem (15pts) 1. Use mathematical

Provide complete solutions

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Answer the following in a separate sheet of paper. Show your solution I. Mathematical Induction and Binomial Theorem (15pts) 1. Use mathematical induction to prove the given statements below. a. 2 . 3 + 2 . 32 +. ... + 2 . 30-1 = 30 - 3 for n 2 1 b. 1+4+ 42+.... +40-1- WIP (4n - 1) for n 2 1 2. Use the Binomial Theorem to expand (2x 4 - 3y 2 ) 5 (2x4 - 3y2)5

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