Exercise.

Exercise.

(a) Show that

Hence, using the induction hypothesis,

show that _{
15
} for all

Exercise.

Either by quoting theorems on boundedness, subsequences, uniqueness of limits, or anything else from the course so far, or by arguing directly from the definition, prove that the following sequences do not converge to any limit.

_{
=2
};
** _{
=(-1)
10000000+1
}**;