Verify, using the definition of convergence of a sequence, that the following se
ID: 3006661 • Letter: V
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Verify, using the definition of convergence of a sequence, that the following sequence converge to the proposed limit. lim n right arrow 1/n = 0 lim n right arrow 1/sqrt n = 0 lim n right arrow (n + 1/n) = 1 lim n right arrow (3n + 1/n + 2) = 3 Use an e argument to explain why the following sequences diverges {a_n} = (-1)^n {s_n} = 1 + (-1)^n how that the constant sequence (a, a, a, a,...) converges to a Show that if lim (a_n) = a, then lim (ca_n) = ca, for all real numbers c. Let f: A right arrow R and let c be a limit point of A. we write lim x right arrow e f(x) = L if and only if for all e > 0, there exist a delta > 0 such that 0Explanation / Answer
Ans-Convergence is a phenomenon in evolutionary computation. It causes evolution to halt because precisely every individual in the population is identical. Full convergence might be seen in genetic algorithms (a type of evolutionary computation) using only crossover (a way of combining individuals to make new offspring). Premature convergence is when a population has converged to a single solution, but that solution is not as high of quality as expected, i.e. the population has gotten 'stuck'. However, convergence is not necessarily a negative thing, because populations often stabilise after a time, in the sense that the best programs all have a common ancestor and their behaviour is very similar (or identical) both to each other and to that of high fitness programs from the previous generations. Often the term convergence is loosely used. Convergence can be avoided with a variety of diversity-generating techniques.
Convergence time is a measure of how fast a group of routers reach the state of convergence. It is one of the main design goals and an important performance indicator forrouting protocols to implement a mechanism that allows all routers running this protocol to quickly and reliably converge.[2] Of course, the size of the network also plays an important role, a larger network will converge slower than a small one.
RIP is a routing protocol that converges so slowly that even a network of a few routers can take a couple of minutes to converge. In case of a new route being advertised, triggered updates can speed up RIP's convergence but to flush a route that previously existed takes longer due to the holddown timers in use. OSPF is an example of a fast-converging routing protocol. A network of a few routers can converge in a matter of seconds.[3]
Certain configuration and hardware conditions will prevent a network from ever converging. For instance, a "flapping" interface (an interface that frequently changes its state between "up" and "down") might cause conflicting information to propagate the network so that routers never agree on its current state. Under certain circumstances it might be desired to withhold routing information details from parts of the network via route aggregation, thereby speeding up convergence of the topological information shared by all
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