right, people are forever posting flawed algebraic proofs to prove 1=0, but they're generally completely obvious. so i'm gonna post some that aren't. these

(note: these require some knowledge of maths)

1.

consider the series 1, -1/2, 1/2, -1/3, 1/3, -1/4, 1/4, -1/5...

from the second term on, each even term is nullified by the term immediately following it (i.e. -1/2 + 1/2 = 0) so the sum of this series-

1 + -1/2 + 1/2 + -1/3 + 1/3 + -1/4 + 1/4 + -1/5... = 1

as 1 is the only term not cancelled by another.

now, if you add brackets, you can get...

(1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) ...

note that

(1/3 - 1/4) = ((4-3)/4.3) = 1/3.4 = 1/12 (. denotes multiplication)

and (1/a - 1/(a+1)) = 1/a(a+1)

so we can rewrite this

1/1.2 + 1/2.3 + 1/3.4 + 1/4.5... = 1 (from before)

but, likewise, we can show that

1/a.(a+1) = -1/a + a/(a+1) <- it works, trust me

and hence that our sequence

1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + ... = 1/2 - 1/2 + 2/3 - 2/3 + 3/4 - 3/4 ... = 0

(obviously)

so this series =0 and 1, so 1=0.

i'm bored, i'll maybe post the other proofs later. see if you can deal with that one.

*are*flawed proofs, but some of them i don't know why, yet (my maths lecturer claims "this week")... so here we go...(note: these require some knowledge of maths)

1.

consider the series 1, -1/2, 1/2, -1/3, 1/3, -1/4, 1/4, -1/5...

from the second term on, each even term is nullified by the term immediately following it (i.e. -1/2 + 1/2 = 0) so the sum of this series-

1 + -1/2 + 1/2 + -1/3 + 1/3 + -1/4 + 1/4 + -1/5... = 1

as 1 is the only term not cancelled by another.

now, if you add brackets, you can get...

(1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) ...

note that

(1/3 - 1/4) = ((4-3)/4.3) = 1/3.4 = 1/12 (. denotes multiplication)

and (1/a - 1/(a+1)) = 1/a(a+1)

so we can rewrite this

1/1.2 + 1/2.3 + 1/3.4 + 1/4.5... = 1 (from before)

but, likewise, we can show that

1/a.(a+1) = -1/a + a/(a+1) <- it works, trust me

and hence that our sequence

1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + ... = 1/2 - 1/2 + 2/3 - 2/3 + 3/4 - 3/4 ... = 0

(obviously)

so this series =0 and 1, so 1=0.

i'm bored, i'll maybe post the other proofs later. see if you can deal with that one.

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