Prove all of the following by induction. Be sure to clearly show your base step, state...

 

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Prove all of the following by induction. Be sure to clearly show your base step, state your induction hypothesis, and clearly show that it is true in the n= k + 1 case. After each statement to be proved, the statement is reiterated in mathematical notation. 1. The sum of the first n odd integers is n². 2. The product n(n+1) is always even. VnEN, )(2i – 1) = n² i=1 VnEN, 3x EZ, n(n+1) = 2x 3. The sum of the first n squares is equal to n(n+1)(2 n(n+1)(2n+1) \n EN₁ n (1²): i=1 = n(n+1)(2n + 1) 6 Prove all of the following by induction. Be sure to clearly show your base step, state your induction hypothesis, and clearly show that it is true in the n= k + 1 case. After each statement to be proved, the statement is reiterated in mathematical notation. 1. The sum of the first n odd integers is n². 2. The product n(n+1) is always even. VnEN, )(2i – 1) = n² i=1 VnEN, 3x EZ, n(n+1) = 2x 3. The sum of the first n squares is equal to n(n+1)(2 n(n+1)(2n+1) \n EN₁ n (1²): i=1 = n(n+1)(2n + 1) 6