KTiaam said:Homework Statement
The nth partial sum of the series
∞
Ʃ an
n=1
is given Sn = 5-1/n
Determine weather the series is convergent or divergent
The Attempt at a Solution
Looked in my book on how to do this one.
couldn't find anything on it.
What i was thinking was find the sum of all n's and finding a pattern and use that as an
however it didnt work, so I am stuck.
The series Sn = 5-1/n converges to the number 5. This can be shown by taking the limit as n approaches infinity, which equals 5.
The convergence or divergence of a series can be determined by taking the limit of the series as n approaches infinity. If the limit exists and is a finite number, the series converges. If the limit does not exist or is infinite, the series diverges.
A convergent series is one whose sum approaches a finite number as more terms are added. A divergent series is one whose sum either approaches infinity or does not approach a finite number as more terms are added.
Yes, the series Sn = 5-1/n can be used to approximate the value of 5. However, as more terms are added, the approximation will become more accurate and approach 5.
To prove the convergence of a series, one can use various methods such as the comparison test, the ratio test, or the integral test. These methods involve comparing the given series to known convergent or divergent series, or using calculus techniques to determine the convergence of the series.