# Thread: Limit of a Sequence

1. ## Limit of a Sequence

Question (1) (a to g) "State the limits of the following sequences, or state that the limit does not exist."

Five of these sequences work something like this (in that they can be represented by an equation):

(b) 5, 4 + 1/2, 4 + 1/3, 4 + 1/4, 4 + 1/5, . . . , 4 + 1/n, . . .

. . . which means I can write

lim x ->(infinity) 4 + 1/n
= 4 + (0)
= 4

However, two of these sequences cannot be expressed with an equation. They are:

(e) 1, 0, 1/2, 0, 1/3, 0, 1/4, 0, . . .

and

(g) 1, 1/2, 1, 1/3, 1, 1/4, 1, 1/5, . . .

I can see that (e) approaches 0, and that (g) does not exist, but how can I show this in writing?

Any help is greatly appreciated.

2. Hello,
Originally Posted by Some_One

However, two of these sequences cannot be expressed with an equation. They are:

(e) 1, 0, 1/2, 0, 1/3, 0, 1/4, 0, . . .
$\displaystyle n \ge 1$

$\displaystyle \left\{\begin{array}{ll} a_{2n}=0 \\ a_{2n-1}=\tfrac 1n \end{array} \right.$

Are the limits the same when n tends to infinity ? (your answer is correct ^^)

and

(g) 1, 1/2, 1, 1/3, 1, 1/4, 1, 1/5, . . .
Try a similar formula as above