Questions: Determine if the series below is a telescoping series. [ sumn=1^inftyleft(10^n+2+19^n+3right) ] Select the correct answer below: The series is telescoping. The series is not telescoping.

Determine if the series below is a telescoping series.
[
sumn=1^inftyleft(10^n+2+19^n+3right)
]

Select the correct answer below:
The series is telescoping.
The series is not telescoping.
Transcript text: Determine if the series below is a telescoping series. \[ \sum_{n=1}^{\infty}\left(10^{n+2}+19^{n+3}\right) \] Select the correct answer below: The series is telescoping. The series is not telescoping.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Series

We are given the series \[ \sum_{n=1}^{\infty}\left(10^{n+2}+19^{n+3}\right). \]

Step 2: Analyze the Terms

The terms of the series can be expressed as \(10^{n+2}\) and \(19^{n+3}\). We need to check if these terms can cancel each other out when the series is expanded.

Step 3: Determine Cancellation

In a telescoping series, most terms cancel out with subsequent terms. However, in this case, the terms \(10^{n+2}\) and \(19^{n+3}\) do not have any terms that will cancel with them in the series.

Step 4: Conclusion

Since there are no cancellations among the terms, we conclude that the series is not telescoping.

Final Answer

The series is not telescoping.

Was this solution helpful?
failed
Unhelpful
failed
Helpful