To find the sum of the given series, we can use the formula for the sum of an arithmetic series:

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) is 1.3 and the last term (l) is 99.101. We need to find the number of terms (n).

To find the number of terms, we can use the formula for the nth term of an arithmetic series:

an = a + (n-1)d

where an is the nth term, a is the first term, n is the number of terms, and d is the common difference.

In this case, the common difference (d) is 1.1. We need to find the value of n when an is equal to the last term (l).

99.101 = 1.3 + (n-1)(1.1)

99.101 = 1.3 + 1.1n - 1.1

99.101 - 1.3 + 1.1 = 1.1n

98.901 = 1.1n

n = 98.901 / 1.1

n ≈ 89.91

Since the number of terms must be a whole number, we round n down to 89.

Now we can substitute the values into the formula for the sum of an arithmetic series:

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

Sn = (89/2)(1.3 + 99.101)

Sn = (89/2)(100.401)

Sn = 4450.445

Therefore, the sum of the series 1.3 + 2.4 + 3.5 + 4.6 + .... + 99.101 is approximately 4450.445.