1. ## convergence of sequence

For Sn given by the following formulas, determine the convergence or divergence of the sequence (Sn). Find any limits that exist:

A) Sn = ( (-1)^n / (n+3) )
B) Sn = ( 2^(3n) / 3^(2n) )
C) Sn = ( (3+n-n^2) / (1+2n) )
D) Sn = 3^n / (n^3 + 5)
E) Sn = n! / (n^n)
F) Sn = (n^2) / n!

2. Is this confusing just as much to others as is to me?

3. No, it is not at all confusing. What have you tried?
What don’t you understand about these?
They are rather standard and simple sequences.

Do you see that (b) is no more than (8/9)^n?
What do you know about (r^n) if |r|<1 ?

4. Originally Posted by luckyc1423
For Sn given by the following formulas, determine the convergence or divergence of the sequence (Sn). Find any limits that exist:

A) Sn = ( (-1)^n / (n+3) )
Here

5. Originally Posted by luckyc1423
For Sn given by the following formulas, determine the convergence or divergence of the sequence (Sn). Find any limits that exist:

B) Sn = ( 2^(3n) / 3^(2n) )
Here

6. Originally Posted by luckyc1423
For Sn given by the following formulas, determine the convergence or divergence of the sequence (Sn). Find any limits that exist:

C) Sn = ( (3+n-n^2) / (1+2n) )
Here

7. Originally Posted by luckyc1423
For Sn given by the following formulas, determine the convergence or divergence of the sequence (Sn). Find any limits that exist:

D) Sn = 3^n / (n^3 + 5)
Here