The formula for calculating the convergence of an infinite series is lim n→∞ (Σ from k=1 to n of a_k). In the case of (2n)/(n^n), this would be lim n→∞ (2n)/(n^n).
To determine the convergence or divergence of an infinite series, we need to use mathematical tests such as the ratio test, root test, or comparison test. These tests help us analyze the behavior of the terms in the series and determine if they approach a finite limit or not.
Yes, the value of an infinite series can be negative. The convergence or divergence of a series is determined by the behavior of its terms, not the overall value of the series.
The value that an infinite series converges to is called the limit or sum of the series. For (2n)/(n^n), the value of the limit depends on the value of n. As n approaches infinity, the value of the limit will approach a certain value or go to infinity or negative infinity.
The convergence of an infinite series is related to its rate of growth. If the terms in the series approach a finite limit, then the series is said to converge, and its rate of growth would be considered slow. If the terms in the series do not approach a finite limit, then the series is said to diverge, and its rate of growth would be considered fast.