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
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.