It equals 1 - but only by a devious definition of "equals".

By normal arithmatic, addition is a binary operation. It only has a meaning when applied to two numbers at a time. The sum of a finite series, say

1 + 2 + 3 + 4 + 5 + 6 + 7

is actually (((((1 + 2) + 3) + 4) + 5) + 6) + 7

This doesn't work with infinite series, as we would have an infinite row of opening brackets.

So.... addition for infinite series is defined as the limit of the sequence formed by adding first one, then two, then three, then four etc.etc. terms together. This sequence never equals 1, it tends to 1, but the series does equal 1, by the definition outlined above.