Final answer:
The minimal number of terms needed to approximate (-1)^k-1 * k^3, where k = 1, to within 0.01 is 4.
Step-by-step explanation:
The minimal number of terms needed to approximate (-1)^k-1 * k^3, where k = 1, to within 0.01 is 4.
We can use the concept of convergence to approximate the given expression. By evaluating the terms of the series up to the fourth term, we can achieve the desired level of accuracy.
Let's calculate the approximate value of the expression using the first four terms:
(-1)^0 * 1^3 + (-1)^1 * 2^3 + (-1)^2 * 3^3 + (-1)^3 * 4^3 = 1 + (-8) + 27 + (-64) = -44
So, the estimate is -44.