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True or False: If E"=D = converges absolutely: then lim /94| < 1True or False: If lim Mlaalthen Zazu Un converges absolutely...

Question

True or False: If E"=D = converges absolutely: then lim /94| < 1True or False: If lim Mlaalthen Zazu Un converges absolutely

True or False: If E"=D = converges absolutely: then lim /94| < 1 True or False: If lim Mlaal then Zazu Un converges absolutely



Answers

True-False Determine whether the statement is true or false. Explain your answer. If a series converges, then either it converges absolutely or it converges conditionally.

Hello. So if we have the sequence of a suburban um converges then we get the limit. So we have a sub n converges right, then we get the limit as an approaches infinity of a suburban minus a suburban plus one or it's going to be equal to zero. So yes, the given statement is true. Um Since if a seven converges, that means the limit as N approaches infinity of a 70. And the limit as N approaches infinity of M plus one is equal to zero. Sort of limit as N approaches infinity of a sub n minus one plus one is equal to just the limit as N approaches infinity of a sub n minus the limit as an approaches infinity of a sub M plus one but that's going to be just zero, just zero minus zero, Which is equal to zero.

Start over problem 15. It says that any bounder sequence converges. This is actually a false statement because even if the CDs is boned, Erred can dive. Watch, for example. It's considered a CDs off minus one, reads to the poor and range in its from one to infinity. So this is actually minus one plus one minus one plus one Ex painted the city's we go on. So all the sequences, uh, owner. But this pregnancies actually. So we cannot say that this if the see the sequence is bounded and we converted can't out. That's where it is a false too.

So here the statement is saying in the sequence as soon as convergent, wow. Mhm. Then limit off has approaches infinity is zero. This is the first of all the false statement. It only says that limit has approaches infinity, essence would be some finite number As n equals two and and is friday night irrational number. So here we can do anything. You just find interesting number, like example 1, 2, 3, 4. It is not necessary to be zero. Yeah.

Taking too. We are given doctors of CDs. You hold square and it converges. So we have to comment on the city's UK. So since the city's convert just like suppose you can me one over UK Square can be won over case square. So if we talked about cities keys from one to infinity, one over case square. So yes, it converges using the PC's just why? Because the B is greater than one. But then if you talk about UK, the UK is one of our que But John okay, is the harmonic progressions where it diverges. But the given statements see, is not UK should also opened would absolutely so the state matters falls since in this case, beverages.


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