#### To determine

**To find:** The wrong calculation.

#### Answer

The third step of the given calculation is wrong.

#### Explanation

**Result used:**

The geometric series
∑n=1∞arn−1
is convergent if
|r|<1
and is divergent if
|r|≥1

**Calculation:**

Consider the given steps,

0=0+0+⋯=(1−1)+(1−1)+(1−1)+⋯=1−1+1−1+1−1+⋯=1+(−1+1)+(−1+1)+⋯

=1+0+0+⋯=1

The series in the third step of the above calculation
1−1+1−1−1+⋯
is the geometric series where
r=−1
.

Here the series
∑n=1∞(−1)n−1
is geometric series where
r=1
.

Thus, the above result, the series
1−1+1−1−1+⋯
is diverges.

That is,
1−1+1−1−1+⋯≠0
.

Hence, the third step of the given calculation is wrong.