Question
Find the first five partial sums of the given series and determine whether the series appears to be convergent or divergent. If it is convergent, find its approximate sum.
(Type an integer or decimal rounded to four decimal places as needed.)
The fifth partial sum is
(Type an integer or decimal rounded to four decimal places as needed.)
The series appears to convergent
To what value does this series converge?
A.
C.
E. The series diverges.
(Type an integer or decimal rounded to four decimal places as needed.)
The fifth partial sum is
(Type an integer or decimal rounded to four decimal places as needed.)
The series appears to convergent
To what value does this series converge?
A.
C.
E. The series diverges.
Ask by Guerrero Bolton. in the United States
Jan 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The series converges to
Solution
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Bonus Knowledge
To find the first five partial sums of the series, we can start by simplifying the expression
Solving for
This is a telescoping series. Now, let’s compute the first five partial sums:
Given the calculated sums:
The series appears to be converging toward a limit, as the partial sums are decreasing and approaching
To determine the convergence value, we can explore the limit of the general term:
Thus, the series converges to:
C.
