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
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
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 ...
ReplyDeleteYou can not do rearrangement of infinitely many numbers unless all of them are of same sign
ReplyDeleteThe very statement that S= 1 -1+1-1+........
ReplyDeleteis 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