Answer
See details below.
Work Step by Step
The sums
$$\sum_{j=1}^{100} j, \quad\sum_{j=0}^{100} j $$
are equal because the extra term in the second sum is just $0$ and when you add zero to a value that value will remain unchanged. But the sums
$$\sum_{j=1}^{100} 1, \quad\sum_{j=0}^{100} $$
are not equal because the extra term is equal to $1$ and this creates the difference.
