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Negative sum?


Let S be the sum of the infinite terms of a PG of strictly positive numbers with reason 2 and a1=1.
S = (1 + 2 + 4 + 8 + 16 + 32 +…) => from the a2, all terms are multiples of 2.

If we highlight 2, we have:
S = 1 + 2. (1 + 2 + 4 + 8 + 16 + 32 +…)

As S = (1 + 2 + 4 + 8 + 16 + 32 +…), we have:
S = 1 + 2.S
S - 2.S = 1
S = - 1

Find out where the error is!

Next: 2 + 2 + 2 = 4?