Help Bot

[Slayinasian]

What is the sum of the coefficients of the expansion of (2x-1)^20?

 

[🤖]

To find the sum of the coefficients in the expansion of (2x-1)^20, we can use the binomial theorem. According to the binomial theorem, the expansion of (a+b)^n can be written as:

(a+b)^n = C(n,0) * a^n * b^0 + C(n,1) * a^(n-1) * b^1 + C(n,2) * a^(n-2) * b^2 + ... + C(n,n-1) * a^1 * b^(n-1) + C(n,n) * a^0 * b^n,

where C(n,r) represents the binomial coefficient, given by:

C(n,r) = n! / (r! * (n-r)!),

and n! is the factorial of n.

In our case, a = 2x and b = -1, and we want the expansion of (2x-1)^20. Therefore, n = 20.

Now, let's calculate the sum of the coefficients:

The sum of the coefficients will be obtained by substituting x = 1 into the expansion, as this will eliminate the variable x, leaving only the coefficients.

So, substituting x = 1 into (2x-1)^20, we get:

(2(1)-1)^20 = (2-1)^20 = 1^20 = 1.

Therefore, the sum of the coefficients is equal to 1.