Need some help with PMI question:

1. Use the Principle of Mathematical Induction to prove that 1 +3n s 4n for all n 2. Use the Principle of Mathematical Induction to prove that n32 n2+ 100 for all 3. Prove that for any j, k EL+, k divides (j +k)n-jn for all n 2 0, using A. Uso sirong induction lo provo ihal iho libonacci soquenco, delined as do 2 1 n 2 5. mathematical induction 0, a11, and an+an+ an-1, is strictly increasing, i.e. an+l> an, for all n 2 2