Saturday 14 July 2012

Find the flaw

Let S = 1-1+1-1+1-1+....................................
Now, clearly the series is divergent and the sum won't exist. But, find a flaw in this argument

S = 1-1+1-1+1-1+.................................... (i)
S =     1-1+1-1+1-1+....................................(ii)
Adding (i) and (ii)


2S = 1
S = 0.5

3 comments:

  1. the limit of S is oscillating between two numbers 0 & 1 ..... and what you have found is just the average of the two .... some kind of expected value ...

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  2. You can not do rearrangement of infinitely many numbers unless all of them are of same sign

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  3. The very statement that S= 1 -1+1-1+........
    is wrong because the series is divergent and equating the series with S makes an assumption that series is convergent and converges to the sum S

    The claim made by Apoorv is also correct

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