Solved: Use the recursive definition of product, together with mathematical induction
Chapter 5, Problem 42(choose chapter or problem)
Use the recursive definition of product, together with mathematical induction, to prove that for all positive integers n, if \(a_{1}, a_{2}, . . . , a_{n}\) and \(b_{1}, b_{2}, . . . , b_{n}\) are real numbers, then
\(\prod_{i=1}^{n}\left(a_{i} b_{i}\right)=\left(\prod_{i=1}^{n} a_{i}\right)\left(\prod_{i=1}^{n} b_{i}\right)\).
Text Transcription:
a_1, a_2, . . . , a_n
b_1, b_2, . . . , b_n
prod_i=1^n (a_i b_i) = (prod_i=1^n a_i) (prod_i=1^n b_i)
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