The great Swiss mathematician Leonhard Euler sometimes reached incorrect conclusions in his pioneering work on infinite series. For example, Euler deduced that 1 =1 – 1+1-1+1-1+·.. 2 and -1 = 1+2+ 4+ 8+ • ·· by substituting x = –1 and x = 2 in the formula 1 = 1+ x + x² + x³ +... 1 What was the problem with his reasoning?

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