Let P(n) be the statement that 2n2 + 6n - 12 is divisible by 4. We wish to prove P(n) by induction for all positive integer values of n. (Note: this statement is provable without induction, but you must use induction to get credit!)Basis step: We will show that P(1) is true.P(1) : 2(12) + 6(1) - 12 is divisible by 4. This works out to "-4 is divisible by 4," which is clearly true.Inductive step: Let k be an integer >= 1, and assume P(k) is true. We must show that P(k + 1) is true.Complete the rest of the inductive step below. Be sure to:Define the inductive hypothesis P(k).Define the statement P(k + 1) that must be shown.Show your algebra throughout the proof. You can use the equation editor in Canvas, or simply write ^ for superscripts and _ for subscripts.
Let P(n) be the statement that 2n2 + 6n - 12 is divisible by 4. We wish to prove P(n) by induction for all positive integer values of n. (Note: this
statement is provable without induction, but you must use induction to get credit!)
Basis step:We will show that P(1 is true
P(1) : 2(12) + 6(1) - 12 is divisible bv 4. This works out to "-4 is divisible
by 4," which is clearly true.
Inductive step: Let k be an integer >= 1, and assume P(k) is true. We must show that P(k + 1) is true
Complete the rest of the inductive step below. Be sure to:
:Define the inductive hypothesis P(k). Defne the statement P(k +1)that must be shown
.Show your algebra throughout the proof.
You can use the equation editor in Canvas,or simply write for
superscripts and-for subscripts.