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Exercise 3. Suppose that |2 < 2. Prove that the series converges absolutely.
Let ne Nj. Prove that n < 2(6(n)).
Problem 5.1.3. Prove by induction on n that (1+ n < n for every integer n > 3.
Let U ? Rmxn. Prove that if UTI-In, then n < m.
Prove using mathematical induction that 3" + 4" < 5" for all n > 2.
QUESTION 13 2 The bra (<) of ø> 15 00(2 i 2 Ob. (1) (2-1) 00 ( 21)
2. (D5) Let n = o(a) and assume that a =bk. Prove that <a >=<b> if and only if n and k are relatively prime.
(c) [5 points] Prove that f(r) [5 p ) = Σ (-1-rn oints Prove that f(x converges uniformly on [-c, c when 0<c<1. lenny
Exercises 4.2 ove that the sequence (1 + z/n)"; n = 1, 2, 3,..., converges uni- ly in Iz <R < , for every R. What is the limit? 1, afdos se converge? diverge?
bn converges 18. Let (an)n=1 and (bn)n=1 be sequences in R. Show that if and lan – an+1 < oo, then anbr converges.