To find the sum of the given series, we can simplify each term and then add them together.

The general term of the series is given by 1/n(n+1). Let's simplify the first few terms:

1/1(1+1) = 1/2
1/2(2+1) = 1/6
1/3(3+1) = 1/12
1/4(4+1) = 1/20

We can see a pattern emerging. The nth term can be written as 1/n(n+1).

Now, let's find the sum of the series:

1/2 + 1/6 + 1/12 + 1/20 + ...

To find a common denominator, we can multiply each term by the least common multiple (LCM) of the denominators, which is 60:

(1/2)(60) + (1/6)(60) + (1/12)(60) + (1/20)(60) + ...

= 30 + 10 + 5 + 3 + ...

Now, we can see that the series is an arithmetic series with a common difference of 5. The sum of an arithmetic series can be found using the formula:

Sn = (n/2)(a + l)

where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

In this case, the first term a = 30 and the common difference d = 5. We need to find the number of terms, which can be calculated using the formula:

l = a + (n-1)d

Rearranging the formula, we get:

n = (l - a)/d + 1

In this case, the last term l is not given, but we can see that the series continues until 1/99(99+1) = 1/9900. Therefore, l = 1/9900.

n = (1/9900 - 30)/5 + 1
= (-29999/9900)/5 + 1
= -5999/9900 + 1
= 1 - 5999/9900
= 391/9900

Now, we can find the sum of the series using the formula:

Sn = (n/2)(a + l)

Sn = (391/9900)(30 + 1/9900)

Simplifying,

Sn = (391/9900)(29700/9900 + 1/9900)
= (391/9900)(29701/9900)
= 115031/326700

Therefore, the sum of the series 1/1×2 + 1/2×3×1/3×4 + ... + 1/99×100 is 115031/326700.