Thực hiện phép tính

To find the value of the given expression, we can use the formula for the sum of a geometric series:

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

Where:
S = sum of the series
a = first term of the series
r = common ratio
n = number of terms

In this case, the first term (a) is (-3/2)^1 = -3/2, the common ratio (r) is -3/2, and the number of terms (n) is 100.

Plugging these values into the formula, we get:

S = (-3/2) * (1 - (-3/2)^100) / (1 - (-3/2))
S = (-3/2) * (1 - 1.2676506e+30) / (1 + 3/2)
S = (-3/2) * (-1.2676506e+30) / (5/2)
S = 1.9014759e+30 / 5
S = 3.8029518e+29

Therefore, the sum of the series is approximately 3.8029518e+29.