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Madhu posted an Question

April 17, 2020 • 14:16 pm

30 points

IIT JAM
Mathematics (MA)

Where all do we apply like this...why we have used this method putting all 2 power n

where all do we apply like this...why we have used this method putting all 2 power n

1 Answer(s)

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V
Vivek kumar

convergent
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Arzoo

Do you get it?
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s....
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then do we have any shortcut to find the leibnitz test
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do we have any shortcuts for leibnitz
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whenever there is alternating series you have to apply leibniz test only. And for leibiz test you have to check all three conditions. You just need practice then you will find it too easy.
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was this helpful?
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Arzoo

I suggest you to see first check if series is geometric and if yes then then apply geometric test and if not then go for other test.Or when they ask about exact sum of series then try to see whether geometric series or any expansion like e^x, logx,sinx...
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Arzoo

Because if series is geometric then we are able to find sum also whereas other tests just tell us about convergence and divergence but not exactly sum.
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M
Madhu

then why do we use geometric series to get the answer
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Arzoo

Madhu you should not get confused with geometric test and ratio test. sometimes ratio test can be applied to questions whereas geometric can't.
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Arzoo

Whenever there is a polynomial or factorial then this ratio test should be apply until it get failed. Whenever exponential type of coefficients then apply nth root test
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why are we comparing with geometric series to get these answers
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why are we applying geometric series to get the answer??
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Ujjawal vishal

option a. see attachment
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then it is equal to infinity...then it is greater than 1..then how is it convergent
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cause here ratio is taken un/un+1...in formula it is un+1/un...so when u take reciprocal it will become 0 i.e.less than 1 and hence convergent
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