To solve this expression, we can simplify each term and then add them together.

The expression can be rewritten as:

(1/1) × 2 + (1/2) × 3 + (1/3) × 4 + ... + (1/99) × 100

Simplifying each term:

2 + 3/2 + 4/3 + ... + 100/99

To add these fractions, we need a common denominator. The least common multiple of the denominators 2, 3, 4, ..., 99 is 2 × 3 × 4 × ... × 99. Let's call this number L.

Now, we can rewrite each fraction with the common denominator L:

(2 × L/L) + (3 × L/L) + (4 × L/L) + ... + (100 × L/L)

Simplifying:

(2L/L) + (3L/L) + (4L/L) + ... + (100L/L)

Now, we can add the numerators together:

2L + 3L + 4L + ... + 100L

This is an arithmetic series with a common difference of L and a first term of 2L. The last term is 100L.

The sum of an arithmetic series is given by the formula:

Sum = (n/2) × (first term + last term)

In this case, n = 100 (the number of terms).

Sum = (100/2) × (2L + 100L)

Simplifying:

Sum = 50 × (2L + 100L)

Sum = 50 × (102L)

Sum = 5100L

Therefore, the sum of the expression 1/1 × 2 + 1/2 × 3 + 1/3 × 4 + ... + 1/99 × 100 is 5100L.