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*