1. Conjecture a formula for the sum XXXXXXXXXX + … + (4n + 1), and prove your conjecture using mathematical induction 2. Prove that XXXXXXXXXX)……(4n- 2) = , for all n ∈ . 3. Indicate for which natural...

1. Conjecture a formula for the sum 5 + 9 + 13 + … + (4n + 1), and prove your conjecture using mathematical induction

2. Prove that

(2)(6)(10)(14)……(4n- 2) =
, for all n ∈
.

3. Indicate for which natural numbers n the given inequality is true. Prove your answers by induction.

(a) n²
≤ n!

(b) n²
≤ 2ⁿ

(c) 2n ≤ n!