If the Binomial Theorem is applied to (x + 1)^n, what is the sum of the coeffici

₹0.0

Question: If the Binomial Theorem is applied to (x + 1)^n, what is the sum of the coefficients of the expansion?

Options:

Correct Answer: 2^n

Solution:

The sum of the coefficients in the expansion of (x + 1)^n is found by substituting x = 1, which gives 2^n.

If the Binomial Theorem is applied to (x + 1)^n, what is the sum of the coefficients of the expansion?

If the Binomial Theorem is applied to (x + 1)^n, what is the sum of the coefficients of the expansion?

Step 1: Understand that the Binomial Theorem helps us expand expressions like (x + 1)^n.
Step 2: The coefficients in the expansion are the numbers in front of each term when we write out (x + 1)^n.
Step 3: To find the sum of all these coefficients, we can substitute x with 1 in the expression.
Step 4: Substitute x = 1 into (x + 1)^n, which gives us (1 + 1)^n.
Step 5: Simplify (1 + 1)^n to get 2^n.
Step 6: Therefore, the sum of the coefficients in the expansion of (x + 1)^n is 2^n.

Binomial Theorem – The Binomial Theorem provides a formula for the expansion of expressions raised to a power, specifically (a + b)^n, where the coefficients can be determined using combinations.
Sum of Coefficients – The sum of the coefficients in a polynomial can be found by evaluating the polynomial at x = 1.