That's easy, just some adjustments and use of "product of three consecutive integers is divisible by 6."
Have a great day!!!

Use the Principle of Mathematical Induction to prove that (2i+3) = n(n + 4) for all n > 1.
Problem 5.1.3. Prove by induction on n that (1+ n < n for every integer n > 3.
Use induction to prove that 0–0 4j3 = n4 + 2n3 + n2 where n > 0.
Problem 7: Prove that for all integers n > 2, n+1 n 10-11 - n n +
8. Use mathematical induction to prove that n + + 7n 15 3 5 is an integer for all integers n > 0.
For all n E N prove that 0 <e- > < 2 k!“ (n + 1)! k=0 Hint: Think about Taylor approximations of the function e".
Exercise 7. Let X be a standard normal random variable. Prove that for any integer n > 0, ELY?"] = 1207) and E[x2n+] = 0.
Please prove this, thanks!
2. Let {xn n21 be a sequence in R such that all n > 0. If ( lim supra) . (lim supー) = 1 Tn (here we already assume both factors are finite), prove that converges.
Suppose that an >0 and bn >0 for all n2N (N an integer). If lim = , what can you conclude about the convergence of an? A. a, diverges if by diverges, and an converges if bn converges. an diverges if by diverges. c. a, converges if be converges. OD. The convergence of an cannot be determined.
Prove by mathematical induction (discrete mathematics)
n? - 2*n-1 > 0 n> 3