4. (P11, Рage 203 (Bernoulli's Inequality) Show that for a natural number n and a nonnegative number b (1+ b)" > 1+ nb. (Hint: In the Binomial Formula, set a = 1.)

Please don't send me the previous posted answer of this question

Show by using construction that n^2+5n+6 is not prime for any n is a natural number.

Number 3. If you had read the previous post, number 3 should read c<a+b. Please only do number 3. Thank you!

3. (Р5, Раge 16; Prove that a <0. (You may have to use Proof by Contradiction and Archimedean Property, Part ii.) Suppose that the number a has the property that for every natural number n, a < 1/n.

Show your work

2. Solve for neN using a product of factors not the ! function on the calculator. Show steps. 9! a) n = 7!3! (n+4)! %3D b) 5 = (n+3)!

10. Prove: A and B countable > Ax B countable.

pls help, thx

pls help, thanks