If Jack exercises for 10 minutes for the first day, then the first term of the sequence is
If he adds 10 minutes to his exercise routine each day, then the sequence is arithmetic since it has a common difference of d=10.
The recursive formula for an arithmetic sequence is
The explicit formula for an arithmetic sequence is
Disturbing the 10 gives
The 7th week is when
Let be two real numbers such that . For , we define and
a) Prove that the sequence is monotonically increasing and that the sequence is monotonically decreasing.
b) Show that the sequences and are bounded.
c) Deduce that the two sequences converge and prove that they converge to the same limit.
determine whether the statement is true or false. Justify your answer. When your attempt to find the limit of a rational function yields the indeterminate form