Anku posted an Question
September 29, 2020 • 13:26 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Determine whether the sequence an is monotonic, bounded and convergent,...pls tell if oossible its upper and lower bound

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    Deepak singh 1

    see , for check monotonic

    cropped8526428671312542100.jpg
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    sir how to apply this fact in question..pls tell that i am not getting

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    I am giving you example , wait

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    see , example..

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    Deepak singh 1 Best Answer

    1. firstly it is sequence not series , 2. if limit exist (finite) implies sequence is convergent .

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    Deepak singh 1 best-answer

    see attached solution

    cropped1573245450423399872.jpg
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    sir i want to know that series is convergent if monotonic increasing and bounded ...is it also. true that if limit n tend to infinity is finite i.e. exists then sequence is convergent pls tell the theorem ..I am missing that

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    sir pls tell

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    this sequence is bounded but not monotonic...

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    feel free to ask again..

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    sir how to know if its monotonic or not...

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    from bound...i.e.-1<=un<=2

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    from boundedness , you can not check monotonic..

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    hoow to check then sir for given sequence..

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    I have attached in attachment , see

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    sir how minimum of cos1/n=0 pls tell

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    sir pls tell

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    see graph ..

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    in the interval (0,1] , minimimum of cos (x) is 0

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    sir but here it can be minimum -1 also..but why not so chosen

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    sir but interval is not given

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    no..

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    then how to determine interval (0,1]

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    here cos (1/n ) and n belongs to N .

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    see , angle of cos is 1/n , from here we get interval (0,1]

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    ok sir got it..

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