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L.sufiya Khanam posted an Question

October 11, 2020 • 12:05 pm

30 points

IIT JAM
Mathematics (MA)

Clarification

plz. give me. an example. for this theorem

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L
L.sufiya khanam

sir this must be mod an-am right, here it is Sn-Sm
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here Sn and Sm are SOPS (sequence of partial sum ) of summation Un.
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L
L.sufiya khanam

sir this must be mod an-am right. why is it sn-sm
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it is right , we take SOPS of series in mod.
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sops?
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when to write an-am and when to write Sn-Sm
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>
Deepak singh 1

another example is take series £1/n^2 is also convergent and follows cauchy's principle of convergence..
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sir for 1/n^2 also show the proof sir?
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>
Deepak singh 1

see attached two examples , it will clear your doubt.
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sir summation of 1/n is 1+1/2+1/3+......+1/n???
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sir I dono proof of 1/n! plz do and send sir
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see proof .
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feel free to ask again
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sir summation of 1/n is 1+1/2+1/3+......+1/n???
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yes..
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sir in that proof I understood everything except the first line .. like how Sn has m also but last term is n! , it has n also , how sir??
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because we have taken n>=m , see again before first line in proof.
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sir in real numbers set Cauchy =convergent and convergent=Cauchy , then 1/n must be Cauchy right as it's convergent???
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this result is for sequence not series..
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Cauchy sequence and Cauchy series is different??
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there is no term like cauchy series . In series we take SOPS of series which is a sequence , then if SOPS of series is cauncy then that series is convergent ...
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okay , in series we take sops , if it is Cauchy it is convergent ,
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then in sequence for R we need to see whether it is convergent , if it's convergent it is cauchy
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I mean if the question is given in sequence and asked whether it is cauchy or no
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