b) Show that the following claim holds when for all n > 1 n (424) >...
(5) Use induction to show that Ig(n) <n for all n > 1.
1. Recall the following theorem. Theorem 1. Let a, b, m,n e N, m, n > 0 and ged(m,n) = 1. There erists a unique r e Zmn such that the following holds. x = a (mod m) x = b (mod n) please show that such solution is unique.
2) (3 pts) Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence 2, ifn=2 T(n) =127G)+n, ifn=2.for k > 1 ISI(72) = n lg n.
1. Show that, for every n > 1: n ka n(n + 1)(2n +1) 6 k=1
6. Use Mathematical Induction to show that (21 - 1)(2i+1) n for all integers n > 1. 2n +1 (5 marks) i=1
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
Show the resistance looking into the base
ro= 0 PA + B + 1)RE >RE (b)
b. Let U2 u~xã. Show that E(b)=n-2 for n > 2. LU
show that if ch[k-n], h[k] > = Ži h*[kn] h[k] = Str], then I Herita, 1 = 1 K:-00 - ICWCTI
Exercise 6. Show that if f(x) > 0 for all x e [a, b] and f is integrable, then Sfdx > 0.