Let S be the sum of the infinite terms of a PG of strictly positive numbers with reason 2 and a_{1}=1.

S = (1 + 2 + 4 + 8 + 16 + 32 +…) => from the a_{2}, 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!*