2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
induction problem prove it P + +8t...n = 12 (n +32 4 + 4 +7 + 3n-1 + (3 -2) = n @ren) = Že - (160)
Prove that the following premise 4. Prove the following: (a) Prove that n is even if and only if n2 6n+5 is odd. (b) Prove that if 2n2 +3n +1 is even, then n is odd.
7 3n-2 n=1
Discrete Math Use division into two cases to prove that for every integer n, 2\n(3n + 1).
2) Prove convergence of In} using the Squeeze lemma: n2-3n+7 a) In = 73 - 4n - 1
2, For each of these sets. A={3n : n E N), B = {r E R : x2 < 7), and C = {x E R : x < 12), (i) Is the set bounded above? Prove your answer.] ( .] ii) Is the set bounded below? Prove your answer answer the following questions:
(a) Prove that, for all natural numbers n, 2 + 2 · 2 2 + 3 · 2 3 + ... + n · 2 n = (n − 1)2n+1 + 2. (b) Prove that, for all natural numbers n, 3 + 2 · 3 2 + 3 · 3 3 + ... + n · 3 n = (2n − 1)3n+1 + 3 4 . (c) Prove that, for all natural numbers n, 1 2 + 42 + 72...
R->H 7. Prove by induction that the following equation is true for every positive integer n. (4 Points) 1. 4lk11tl + 2K ²+ 3k 4k+4+H26² +3k {(4+1) = (40k41) 40) j=1 (4i + 1) = 2 n 2 + 3n 2K?+75 +5 21 13 43 041) 262, ultz
estimate error ∞ 4n (n + 7)3n n = 1