• Sequence
• Arithmetic
• Geometric
• nth
• Limit
• P.
• Monotone
• Bounded
• Convergent

1The limit, if it exists, is unique.

2If a sequence, a_n, has a limit, all the subsequences have the same limit as a_n.

3 All convergent sequences are bounded.

4There are bounded sequences that are not convergent.

5 All the monotone and bounded sequences are convergent.

6There are convergent sequences that are not monotonous.

Rules of Limits

lim (a_n + b_n) = lim (a_n) + lim (b_n)

lim (a_n − b_n) = lim (a_n) − lim (b_n)

lim (a_n · b_n) = lim (a_n) · lim (b_n)

lim (a_n : b_n) = lim (a_n) : lim (b_n)

lim k · a_n =k · lim a_n

lim a_n^k = (lim a_n)^k

lim log_a a_n = log_a lim a_n

By applying these rules, the following cases are presented:

• 
• 
•