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Vijay posted an Question

September 28, 2021 • 18:52 pm

30 points

IIT JAM
Mathematics (MA)

Is the converse true?

please send the solution to the problem given in the attachment.

2 Answer(s)

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Anonymous User

check
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Prerna chaudhary 1

see
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doubt
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1,2,1,3,1,4,1,5,1,6,1...so on and f_n={1/n if n is even { n is n is odd. It will also not converge but having a lim pt. ie 0
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Prerna chaudhary 1

simply on the bases of finite limit and unique limit point we can't says that sequence is convergent it should be bounded also
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do you have an example supporting your theorem?
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Prerna chaudhary 1

theorem... A sequence is convergent iff it is bounded and has a unique limit point
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Deepak singh 1 Best Answer

Refer attachment
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Arpan pal

yes it's true because we know the definition of the convergence of a sequence that a sequence {Sn}is said to be convergent to be a finite limit if for pre-assigned £>0,there exists a natural number k such that |Sn-l|<£ for all n≥k i.e.,limSn=l
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Anonymous User

yes
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how do you know that?
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T