So here my thought was: if i see each two terms it will be a GP which is like 1/2+1/4+1/8+....
So sum of it will be 1 is it conditionally convergence?
#Convergence
rancid bone
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So here my thought was: if i see each two terms it will be a GP which is like 1/...
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rancid bone
And if i look at even add terms it converge to 1 and
balmy drum
the general term doesn't converge to 0
rancid bone
the general term doesn't converge to 0
How did you check it?
Should I apply leibeinz test?
balmy drum
it requires that the absolute value of the general term converge to 0
this is not true, so the test doesn't apply
balmy drum
How did you check it?
are you familiar with definition of limit?
rancid bone
Yes cauchy convergence
balmy drum
you have 1 infinitely often in the general term
rancid bone
Necessary condition
balmy drum
so the general term can't converge to 0
A,B,C are automatically out
include your definition of "oscillatory" to check the last condition
you could also analyse the partial sum up to the first even number of digits
so that would
1-1/2
1-1/2+1-3/4
etc
and see what the limiting behaviour is
balmy drum
How did you check it?
if a sequence converges to 0, then every subsequence also converges to 0
contrapositively, if at least one subsequence doesn't converge to 0, then the sequence itself also doesn't converge to 0
rancid bone
yes it is D
rancid bone
if a sequence converges to 0, then every subsequence also converges to 0
but is it applied to series?
i meant the sequence 1+1+1+1... it converges to 1 but the series tends to infinity no?
balmy drum
the general term of a series forms a sequence
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