Determine whether the sequence converges or diverges.If it converges, find the limit.
To find: Whether the sequence converges or diverges and to obtain the limit if the sequence converges.
The sequence converges and its limit is 3.
The sequence is an=3nn+2.
If an is sequence and limn→∞an exists then the sequence an is convergent otherwise it is divergent.
Obtain the limit of the sequence to investigate whether the sequence converges or diverges.
Divide the numerator and the denominator by n.
Redefine the terms of the numerator and the denominator as follows:
Apply the property limn→∞(kna)=0 and simplify the numerator and the denominator.
Since limn→∞an exist and by using the definition of the sequence, it can be concluded that the sequence converges to the limit 3.
Therefore, the sequence converges to the limit 3.