Determine whether the sequence converges or diverges.If it converges, find the limit.
Whether the sequence is converges or diverges and obtain the limit if the sequence is converges.
The sequence is converges and its limit is 0.
The sequence is
is sequence and
is exists then the sequence
is convergent otherwise it is divergent.
is converges to zero when
limn→∞rn=0 if −1<r<1
Obtain the limit of the sequence to investigate whether the sequence is converges or diverges.
limn→∞an=limn→∞(3n7−n) =limn→∞(3n7n) =limn→∞(37)n
and by using the result,
is exist and by using the definition of the sequence, it can be concluded that the sequence is converges to the limit zero.
Therefore, the sequence is converges to the limit 0 when