c] lim s, = 0 iff lim |s„=0 %3D %3D
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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Math 4303 Homework Section 4.1 Convergence
1. Write out the first seven terms of the sequence dn
2n +1
%3D
3n-1
2. Using only Definition 4.1.2 (N-ɛ definition of convergence), prove the following:
k
a] lim
- = 0
kER
4n +1
b] lim
no n+3
= 4
6n? +3n
= 3
no 2n? -5
c] lim
sin( n)
=D0
d] lim
3. Prove or provide a counterexample for the following:
a] If (s,) converges then (s) converges.
b] If (s,) converges then (s,) converges.
c] lim s, = 0 iff lim |s„ =0
4. Suppose that lim s, =0 and suppose that (t, ) is a bounded sequence. Show that lim s,t, = 0
5. Suppose that (x,), (y, ), and (=,) are sequences such that x, Sy, S=, n and lim x, = L = lim =
Show that lim y, = L
6. Suppose that lim s. =s where s > 0. Prove that there exists a natural number N, such that
if n> N, then s, > 0
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