For the sequence, determine the convergence or divergence. If it converges, find the limit.

a) {an}={1+(-1)^n}

Question

For the sequence, determine the convergence or divergence. If it converges, find the limit.

a) {an}={1+(-1)^n}

experimentx · Answer

the sequence does not converge

experimentx · Answer

the sequence diverges in the sense that it does not converge.

anonymous · Answer

it diverges because the limit goes to infinity when you apply it, correct?

experimentx · Answer

no ... it is an example of oscillating sequence. do you know what is limit point/cluster point/adherent point?

anonymous · Answer

no we haven't done that in class.

experimentx · Answer

http://math.stackexchange.com/questions/182907/limit-point-versus-limit-and-implications-for-convergence

anonymous · Answer

okay i have another question, same type just difference sequence.

experimentx · Answer

then this is a bit difficult. A limit point is something around which you get infinitely many points of the sequence. you notice this whole value is either 0 or 2.
it means you have infinitely many 0 and infinitely many 2. but a convergent sequence can have only one limit point. therefore it does not converge.

if the limit does not converge then it diverges.