If the Binomial Theorem is used to expand (x + 1/x)^6, what is the term containi

If the Binomial Theorem is used to expand (x + 1/x)^6, what is the term containing x^0?

If the Binomial Theorem is used to expand (x + 1/x)^6, what is the term containing x^0?

Step 1: Identify the expression to expand using the Binomial Theorem, which is (x + 1/x)^6.
Step 2: Recall the Binomial Theorem formula: (a + b)^n = Σ (nCk * a^(n-k) * b^k) for k = 0 to n.
Step 3: In our case, a = x, b = 1/x, and n = 6.
Step 4: We need to find the term where x^0 appears. This happens when the power of x is zero.
Step 5: Set up the equation for the powers: n - k = 0, which means k = n.
Step 6: Substitute n = 6 into the equation: k = 3 (since we want the term where x^0).
Step 7: Calculate the term using k = 3: 6C3 * (x)^(6-3) * (1/x)^3.
Step 8: Simplify the term: 6C3 * x^3 * (1/x)^3 = 6C3 * x^3 * (1/x^3) = 6C3 * 1.
Step 9: Calculate 6C3, which is 20.
Step 10: Therefore, the term containing x^0 is 20.

Binomial Theorem – The Binomial Theorem provides a formula for expanding expressions of the form (a + b)^n, where the coefficients of the terms can be determined using combinations.
Finding Specific Terms – To find a specific term in the expansion, one must identify the appropriate value of k that results in the desired power of x.
Combinatorial Coefficients – The coefficients in the expansion are determined using binomial coefficients, represented as nCk.