I don’t know the name of this proof. I also don’t know how I came across this one. This proof is correct on the assumption that 2 times infinity is the same as infinity. ln(2) contains infinite terms while 2ln(2) contains two times the infinite terms.

ln(2) = 1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 + 1/7 – 1/8 + . . . .

2ln(2) = 2(1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 + 1/7 – 1/8 +. . . .)

2ln(2) = 2 – 1 + 2/3 – 1/2 + 2/5 – 1/3 + 2/7 – 1/4 + . . . .

2ln(2) = 1 + 1/3 – 1/2 + 1/5 + 1/7 – 1/4 + . . . .

2ln(2) = 1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 + . . . .

2ln(2) = ln(2)

2 * .693 = 1 * .693

2 = 1

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