Question

Enter the value for each variable:

a = 1,
b = -0.02,
n = 5
Problem: Evaluate the first four terms in the binomial expansion.
1st term =
2nd term =
3rd term =
4th term =

Answer 1

The first four terms of the binomial expansion for (1 - 0.02)^5 using the binomial theorem are 1, -0.1, 0.002, and -0.00008.

Step-by-step explanation:

The student is asking about evaluating the first four terms of a binomial expansion using the binomial theorem. In this case, we have a = 1, b = -0.02, and n = 5. Using the formula for the binomial expansion, which is (a + b)^n = a^n + n*a^(n-1)*b + n*(n-1)/2! * a^(n-2)*b^2 + n*(n-1)(n-2)/3! * a^(n-3)*b^3 + ..., we can calculate the terms.

1. 1st term = 1^5 = 1
2. 2nd term = 5*1^4*(-0.02) = -0.1
3. 3rd term = 5*4/2!*1^3*(-0.02)^2 = 0.002
4. 4th term = 5*4*3/3!*1^2*(-0.02)^3 = -0.00008