CHAPTER 36
Infinite Sequences
In Problems 36.1-36.18, write a formula for the nth term «„ of the sequence and determine its limit (if it exists). It is
understood that n = 1,2,3,....
36.1
Clearly.
36.2
There is no limit.
36.3
1,-I, !,-!,....
36.4
Clearly there is no limit.
1,0,1,0,1,0,
36.5
36.6
36.7
36.8
36.9
36.10
Note that this depends on the continuity of In x at x = 1.
305
since
In
In
Infinite Sequences
In Problems 36.1-36.18, write a formula for the nth term «„ of the sequence and determine its limit (if it exists). It is
understood that n = 1,2,3,....
36.1
Clearly.
36.2
There is no limit.
36.3
1,-I, !,-!,....
36.4
Clearly there is no limit.
1,0,1,0,1,0,
36.5
36.6
36.7
36.8
36.9
36.10
Note that this depends on the continuity of In x at x = 1.
305
since
In
In