Compute the values of the product (¹ + ²) (¹ + ²) (¹ + - ) ... (¹ + ²) 1+ 1+ for small values of n in order to conjecture a general formula for the product. Fill in the blank with your conjecture. (¹ + ³ ) (¹ + ² ) (¹ + ³ ) · · · (¹ + ²- ) [ 1+ Prove your conjecture by mathematical induction. Proof (by mathematical induction): Let P(n) be the equation (1+ ·( ¹ + ² ) ( ¹ + ² ) (¹ + — ) --- ( ¹ + ²+ ) [ Show that P(1) is true: Select P(1) from the choices below. O P(1) = 1 We will show that P(n) is true for every integer n 2 1. 0 (¹ + 1) (¹ + ²) (¹ + 3) (¹ + )-1+2+3 1+ 01+1-1+1 ○ P(1) -1 + The selected statement is true because both sides of the equation equal the same quantity. Show that for each integer kz 1, if P(k) is true, then P(K + 1) is true: Let k be any integer with k 2 1, and suppose that P(K) is true. The left-hand side of P(K) is (1 + 1) (¹ + 1) (¹ + 1) - ( [ [The inductive hypothesis is that the two sides of P(k) are equal.] We must show that P(x + 1) is true. The left-hand side of P(x + 1) is (1 + ) ( ¹ + ² ) ( ¹ + ² ) · · ( [ the left-hand and right-hand sides of P(k+ 1) are simplified, they both can be shown to equal and the right-hand side of P(k+ 1) is . Hence P(k+ 1) is true, which completes the inductive step. and the right-hand side of P(k) is . After substitution from the inductive hypothesis, the left-hand side of P(k+ 1) becomes (-Select-V 2). (1+2+1). Wh When