I was going to start a new thread but I decided to tagg along this one. Okay I have two problems. Please explain this clearly. Im really having a hard time understanding this stuff.

**Prove by induction that for any x, if x 1, then 3n 1 + 2n.**
Step 1:For x =, P() = [(3 × 1) = 1 + 2].The base case is (Type T/F.).Step 2:For k suppose that 3k

1 + 2k is(Type T/F.)Step 3:Add in the termNow the expression is(k + 1)

1 + 2(k + 1)This becomes3k +

(1 + 2) + 2We conclude the statement is(Type T/F.)because the left side increases more than the right.

**Prove by induction that for any x, if x 1, then 5n 1 + 4n .**
Step 1:For x = 1, P(1) = [(5 × 1) = 1 +].The base case is (Type T/F.).Step 2:For k suppose that 5k

1 + 4k is(Type T/F.)Step 3:Add in the termNow the expression is(k + 1)

1 +(k + 1)This becomes5k +

(1 + 4) + 4We conclude the statement is (Type T/F.)because the left side increases more than the right.

Thank You!