1=21=2 | Continued fraction fallacy

It’s easy to check that for any natural n
n+1n=12n+2n+1.

Now,

1=121=12121=1212121=121212121==1212121212,

2=1232=121243=12121254=1212121265==1212121212.

Since the right hand sides are the same, hence 1=2.

Answer

A variant: note that
1=0+1=0+0+1=0+0++0+1=0+0+0+
and
2=0+2=0+0+2=0+0++0+2=0+0+0+
“Since the right hand sides are the same”, this proves that 1=2.

Attribution
Source : Link , Question Author : Mher , Answer Author : B. Mehta

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