if possible solve all 7

Use mathematical induction to prove the followings: 1. 1.1!+22!+33!++nn!=(n+1)!1 for all n1 [15pts. 2. 12+2223+2425++(1)n2n=32n+1(1)n+1 for all n0 [15pts] 3. n3>n2+3 for all n2 [15pts. 4. 1+3+9+27++3n=23n+11 for all n0 [15 pts.] 5. 1+4+7+10++(3n2)=2n(3n1) for all n1 [15 pts.] 6. j=n2n1(2j+1)=3n2 for all positive integers n. [15 pts.] 7. Let a1=2,a2=9, and an=2an1+3an2 for n3. Show that an3n for all positive integen n. [10 pts.]