let's firstly convert the mixed fractions to improper fractions and then to do away with the denominators, let's multiply both sides by the LCD of all denominators.
Which of the following is not a real number?
1 answer:
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Assuming the series is
The series will converge if
We have
So the series will certainly converge if
, but we also need to check the endpoints of the interval.
If
, then the series is a scaled harmonic series, which we know diverges.
On the other hand, if
, by the alternating series test we can show that the series converges, since
and is strictly decreasing.
So, the interval of convergence for the series is
.
The series will converge if
We have
So the series will certainly converge if
If
On the other hand, if
and is strictly decreasing.
So, the interval of convergence for the series is