Please solve fully
Determine whether the geometric series is convergent or
divergent. If it is convergent, find its sum.8 − 11 +
121
8
−
1331
64
+
Step 1
To see 8 − 11 +
121
8
−
1331
64
+ as a geometric series, we
must express it as
∞
ar n − 1
n = 1
.
For any two successive terms in the geometric series
∞
ar n − 1
n = 1
, the ratio of...
Let {an} be a bounded sequence. In this question,
you will prove that there exists a convergent subsequence.
Define a crest of the sequence to be a
term am that is greater than all subsequent terms. That is,
am > an for all n > m
(a) Suppose {an} has infinitely many crests. Prove
that the crests form a convergent subsequence.
(b) Suppose {an} has only finitely many crests. Let
an1 be a term with no subsequent crests. Construct a...