Prove the following statement by mathematical induction. For every integer n 20, 1-2¹-n-2+2+2. Proof (by mathematical induction): Let P(n) be the equation 2n+2+2 Σ We will show that P(n) is true for every integer n 2 0. Show that P(0) is true: Select P(0) from the choices below. 0+1 O 1-2¹-1-2¹ +2 +2 01-2-0-20+2+2 02=0-20+2+2 IME IME IME IME 1-2-0-20+2+2 n+1 The selected statement is true because both sides of the equation equal the same quantity. Show that for each integer k ≥ 0, if P(k) is true, then P(x + 1) is true: Let k be any integer with k≥ 0, and suppose that P(K) is true. Select the expression for the left-hand side of P(k) from the choices below. 01-2 1-2k +1 The right-hand side of P(k) is The inductive hypothesis states that the two sides of P(k) are equal.] (k+1)+1 We must show that P(x + 1) is true. The left-hand side of P(x + 1) isi-2¹. When the final term of eft-hand side of P(k+ 1) becomes (k+12+1 ¡-2¹ is written separately, the result is 1-2²-²1-2² + - (* + 2)2* + 2). When the left-hand and right-hand sides of P(k+ 1) are simplified, they both can be shown to equal (k+1)+1 Thus both the basis and the inductive steps have been proved, and so the proof by mathematical induction is complete.] . The right-hand side of P(x + 1) is +2. Hence P(x + 1) is true, which completes the