It’s easy to check that for any natural n
n+1n=12−n+2n+1.Now,
1=12−1=12−12−1=12−12−12−1=12−12−12−12−1=…=12−12−12−12−12−…,
2=12−32=12−12−43=12−12−12−54=12−12−12−12−65=…=12−12−12−12−12−….
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
