To find the value of C, we need to calculate the sum of the series:

C = 1 + 2 + 2^2 + 2^3 + 2^4 + ... + 2^100

This is a geometric series with a common ratio of 2. The sum of a geometric series can be calculated using the formula:

S = a * (1 - r^n) / (1 - r)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 1, r = 2, and n = 100. Plugging these values into the formula, we get:

C = 1 * (1 - 2^100) / (1 - 2)

Simplifying further:

C = (1 - 2^100) / (-1)

Since the denominator is -1, we can multiply both the numerator and denominator by -1 to get:

C = (2^100 - 1) / 1

Therefore, the value of C is equal to 2^100 - 1.