find the limit of the sequence if it exists
tn= 6/n
To find the limit of the sequence tn = 6/n, we need to evaluate the expression as n approaches infinity.
To do this, we can use the concept of the limit. The limit of a sequence represents the value that the terms of the sequence approach as the index n becomes very large.
In this case, as n approaches infinity, the value of 6/n becomes very small because the denominator becomes larger and larger. We can see this by substituting some large values for n:
t1 = 6/1 = 6
t10 = 6/10 = 0.6
t100 = 6/100 = 0.06
t1000 = 6/1000 = 0.006
...
As you can see, as n increases, the value of tn becomes arbitrarily close to 0. In other words, the terms of the sequence get smaller and smaller.
Based on this observation, we can conclude that the limit of the sequence tn = 6/n as n approaches infinity is 0.
Therefore, the limit of tn as n approaches infinity exists and is equal to 0.