induction question, thanks. (15 points) Prove by induction that for an odd k > 1, the number 2n+2 divides k2" – 1 for all every positive integer n.
(2) Prove by induction that for all integers n > 2. Hint: 2n-1-2n2,
.n= n(n-1)(n+1) for all n > 2. 12. Use induction to prove (1 : 2) +(2-3)+(3-4) +...+(n-1).n [9 points) 3
Use induction to prove that for m > 5, 5m > 25m?.
Use induction to prove that 0–0 4j3 = n4 + 2n3 + n2 where n > 0.
Problem 44) Prove: n!> 2" for n24. Problem 45) Prove by induction: For n>0·AT- i=1
Problem 5.1.3. Prove by induction on n that (1+ n < n for every integer n > 3.
Use induction and Pascal's identity to prove that (7) = 2" where n > 0.
Prove each problem, prove by induction 3) Statementn-1 5 25(2m-1) forn2 1 4 Statement Suppose: bo1 . b,-2b-1 + 1 for t 1 en fort >
1. Show that, for every n > 1: n ka n(n + 1)(2n +1) 6 k=1