Need help with problem 24, (discrete structures) Chapter 2, section 2

In Exercises 3-26, use mathematical induction to prove that the statements are true for every positive integer, Host: In the algebra part of the proof, if the final expression you want has factors and you can pull those factors out carly, do that instead of multiplying everything out and getting some humongous expression.) 3.1+5+9++ (4-3) ( 2-1) (n+1) + 1X + 2) 4. ! +3 +6+... 2 6 5.4+ 10 + 16 +++ (6 -- 2) =(3+1) 6. 5 + 10 + 15 + ... + 5 = Sm+ 1) 2 (n + 1)(2+1) 7.12 + 2 + + 6 (n + 1) 4 9.1 + 32 + ... + (2n-1) = (21-1/2 + 1) 3 10.1' + 2+ + + 1)2 + 1)(3x + 3x - 1) 30 in + 1)(2x + 7) 11.1.3 +2.4 +3:5++ ( + 2) = 121 + a +...+! for a 0.01 14 + 1 1 1 13 + 3.4 nin +1) +1 1 1 1 1 + +++ 3.5 5.7 (2-1X2+) 15.12 - 22 + 32 - 4 + ... + (-1- (-1)"+1) 2 16. 2 + 6 + 18+ ... + 2-3"-1 - 3-1 17.22 + 47+...+(21) 2 + 1X2 + 1) 3 18.1.2+2-22 +3.2++2 -- 1)2*** + 2 in + 1 + 2) 19.1.2+2-3 + 3.4 + ... + ( + 1) 124 Proots, Induction and Number Theory 4 (n + 1)(n + 2)(n+3) 20.1.2-3 + 2-3.4 + 1 + (n + 1) + 2) = 1 1 21 7.10 ( - 24 + 1) 3n+1 22.1. 1! + 2.2!+ 3.31 +*+n! =(n + 1)! - 1 where nt is the product of the positive integers 1 1 1+4 4.7 +++ from 1 to 23.1+ 4 + 4 + + 4 3 24.1 + x +++ where is any integer > 1