cloveryeah said:Homework Statement
summation n from 1 to inf, 1/ln(n+5) converge or diverge
Homework Equations
The Attempt at a Solution
1/ln(n+5) > 1/n (from n=2 to inf)
and i proved that it diverges by comparison test, am i correct?
i am thinking that as my prove is n from 2 to inf not from 1 to inf
can i still use this prove?
The definition of series converge is when the terms of a series approach a finite limit as the number of terms increases. In other words, the sum of the terms of the series approaches a specific value as more terms are added.
One way to determine if a series converges or diverges is by using the limit comparison test, where the series is compared to a known convergent or divergent series. Another method is the integral test, where the series is compared to an improper integral.
Absolute convergence occurs when the series converges regardless of the order in which the terms are added. On the other hand, conditional convergence occurs when the series only converges if the terms are added in a specific order.
Yes, a series can converge to a negative value. This happens when the sum of the terms of the series approaches a negative number as the number of terms increases. This type of convergence is known as oscillating convergence.
Some common examples of convergent series include the geometric series, where the ratio between consecutive terms is constant, and the telescoping series, where most of the terms cancel out. Divergent series include the harmonic series, where the denominator of each term is an increasing sequence, and the alternating harmonic series, where the signs of the terms alternate between positive and negative.