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###### Vijay posted an Question
September 28, 2021 • 13:22 pm 30 points
• IIT JAM
• Mathematics (MA)

# Is the converse true?

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

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check

• ##### Prerna chaudhary 1

see

doubt

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

• ##### 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

do you have an example supporting your theorem?

• ##### Prerna chaudhary 1

theorem... A sequence is convergent iff it is bounded and has a unique limit point

• ##### Deepak singh 1 Best Answer

Refer attachment

• ##### 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

• ##### Anonymous User

yes

how do you know that?

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