1. ## Induction proof

1)
A) Find k>0 and m element of N so that 7n^3 + 13n <= kn^3 for all integers n >= m.... take k = 7.0052 and find the corresponding value of m

B) find k > 0 and m element of N so that n^3 - 3n >= kn^3 for all integers
n >= m

2) Find an example of each of the following
A) A convergent sequence of rational numbers having an irrational limit
B) A convergent sequence of irrational numberse having a rational limit.

2. For #2
A) Let [x_1]=1. Then if n>1, let [x_n]={1+(2/[x_(n-1])}/2.

B) Let [y_n]=sqrt(2)/n

3. Do you have any ideas on #1?

4. Originally Posted by learn18
1)
A) Find k>0 and m element of N so that 7n^3 + 13n <= kn^3 for all integers n >= m.... take k = 7.0052 and find the corresponding value of m
.
You can take k=8.

7n^3+13n<=8n^3 for sufficiently large n.