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soul
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I know it is easy but I need help. lim(n->infinity)((-1)^n)/n diverge or converge?and why?
p.s: question may not be understandable. Sorry for that.
p.s: question may not be understandable. Sorry for that.
Feldoh said:lim(n->infinity)((-1)^n)
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lim(n->infinity)n
Couldn't you just evaluate the series this way?
Are you just looking whether that limit exists, or your original question requires sth else, like whether the series with the general term a_n=(-1)^n /n converges or not?soul said:I know it is easy but I need help. lim(n->infinity)((-1)^n)/n diverge or converge?and why?
p.s: question may not be understandable. Sorry for that.
Well, to show that a series is convergent you first need to determine whether it is monotonic or not, then show that it is bounded. Or if the limit of that sequence exists then from a theorem we conclude that it is convergent also.soul said:This is the original question. If you want to check it, you can look at p.757 of Thomas's calculus (question 24). It says that find whether this sequence is convergent or not. If convergent find the limit of it?
soul said:I know it is easy but I need help. lim(n->infinity)((-1)^n)/n diverge or converge?and why?
p.s: question may not be understandable. Sorry for that.
The formula is Lim (n→∞)((-1)^n)/n.
In this formula, (-1)^n is an alternating sequence that switches between positive and negative values as n increases.
A sequence converges if its terms approach a single finite value as n increases without bound. It can also be thought of as the sequence "settling" towards a specific value.
The sequence Lim (n→∞)((-1)^n)/n does not converge because the terms do not approach a single finite value as n increases without bound. Instead, it oscillates between positive and negative values.
The (-1)^n in this formula represents the alternating nature of the sequence. It is responsible for the sequence not converging and instead oscillating between positive and negative values.