What is the value of the term containing x^5 in the expansion of (x + 1/2)^8? (2
Practice Questions
Q1
What is the value of the term containing x^5 in the expansion of (x + 1/2)^8? (2020)
8
56
112
128
Questions & Step-by-Step Solutions
What is the value of the term containing x^5 in the expansion of (x + 1/2)^8? (2020)
Step 1: Identify the expression we are expanding, which is (x + 1/2)^8.
Step 2: Recognize that we want the term that contains x^5 in the expansion.
Step 3: Use the binomial theorem, which states that the general term in the expansion of (a + b)^n is given by C(n, k) * a^(n-k) * b^k, where C(n, k) is the binomial coefficient.
Step 4: In our case, a = x, b = 1/2, and n = 8. We need to find the term where the power of x is 5, which means k = 8 - 5 = 3.
Step 5: Calculate the binomial coefficient C(8, 5), which is the same as C(8, 3). This is calculated as 8! / (3! * (8-3)!) = 56.
Step 6: Now, substitute the values into the term formula: C(8, 3) * (x^5) * (1/2)^3.
Step 7: Calculate (1/2)^3, which is 1/8.
Step 8: Multiply the binomial coefficient by (1/2)^3: 56 * (1/8) = 7.
Step 9: Therefore, the value of the term containing x^5 is 7.
