0
votes
0answers
9 views

Cauchy sequences, not converging to zero [migrated]

True or False? If {x_n} and {y_n} are Cauchy and x_n + y_n > 0, for all natural n, then {1/(x_n + y_n)} cannot converge to zero. attempt:False: If both sequences are Cauchy, then they are convergent ...
1
vote
0answers
119 views

Limit of sequence

I tried to calculate the following limit $$\lim_{n\to\infty}n\sin(2\pi en!)$$ Mathematica gets ...
9
votes
1answer
337 views

Is it possible to find a limit of a sequence given by its recurrence relation?

I need to calculate a limit of a sequence given by its recurrence relation. I tried the following: ...
-3
votes
1answer
157 views

Limit of a subsequence

I am trying to calculate limit for a subsequence <${ a }_{ {n }^{ 2} }$> because I was trying to see that limits of sequences and subsequences are both same. I was able to generate the sum for ...