Proof that 0 = 1 using Infinite Series - Can you Find the Mistake?

Proof that 0 = 1 using Infinite Series - Can you Find the Mistake?

[duckymomo]

It’s not absolutely convergent, Riemann rearrangement theorem doesn’t apply.

[erakanimthatiwa]

the 1s in the third step are not balancing with the once in fourth step. if we solve it with balance number of 1s we will see that we will have an extra -1 at the end which makes it a zero

[chadjensenster]

you changed the order of operation when you moved the parenthesis. Changing the order of operation is important for addition/ subtraction. 1-(3-1) != 1-3-1

[brepi]

infinity - infinity is indeterminant, not 0. This basically says "∞=∞+1, so minus both sides by ∞, and 0=1"

[ALAsilTech]

The infinite series of (-1+1) still needs a -1 to be a correct as in the 3rd line it starts with +1 so it should ends with -1 not +1 as assumed when written it in 4th line in terms (-1+1)

[duckymomo]

The value of this series can also be assigned as 1/2.

[silverspike]

1:20 you wrote it the wrong way, you wrote a 1 too much