Limits

[sTEMON]

for the worksheet im doing currently it asks me the following question above, i can undersand the basics of proofs, however im not sure how to do this question, i dont have any current workings, any idea? on what i do, thanks

 

[Dr.Peterson]

Think of a sequence that converges. Call that x_n.

Think of a sequence that does not. Call that z_n.

Now (for part a) you want to make z_n = y_n/x_n, so y_n = x_n z_n. Try to arrange things so that y_n will converge.

You "workings" will be attempts to do this, not some formula you can follow. You have to try things, in order to get familiar with how sequences work; I can't give you the insight you need, which comes from experience. (This is like children learning how the world works by playing with it.)

Show some attempts, and we can try to guide your thinking.

 

[lev888]

Please post examples of a sequence that converges and one that doesn't.

 

[sTEMON]

Think of a sequence that converges. Call that x_n.

Think of a sequence that does not. Call that z_n.

Now (for part a) you want to make z_n = y_n/x_n, so y_n = x_n z_n. Try to arrange things so that y_n will converge.

You "workings" will be attempts to do this, not some formula you can follow. You have to try things, in order to get familiar with how sequences work; I can't give you the insight you need, which comes from experience. (This is like children learning how the world works by playing with it.)

Show some attempts, and we can try to guide your thinking.

oh ok i think i understand, just to make sure am i selecting two random sequences?

 

[Dr.Peterson]

You can create them at will.

Not technically "random", but whatever you wish in order to obtain an example.

 

[Steven G]

Hint for part b. You can get away with finding just one sequence. Just use it twice.