Question

The binomial theorem says that for any positive integer n, (a + b)^n = nC0 * a^n + nC1 * a^(n-1) * b + nC2 * a^(n-2) * b^2 + ... + nCn * b^n. The rth term in the binomial expansion of (a + b)^n is:

a) nCr - 1 * a^n - (r - 1) * b^(r - 1)
b) nCr * a^n - r * b^r
c) nCr * a^(n - r) * b^r
d) nCr - 1 * a^(n - (r - 1)) * b^(r - 1)

Answer 1

The rth term in the binomial expansion of (a + b)^n is: c) nCr * a^(n - r) * b^r. Hence the correct answer is option C

Step-by-step explanation:

The rth term in the binomial expansion of (a + b)^n is:

c) nCr * a^(n - r) * b^r

The formula given in the question: (a + b)^n = nC0 * a^n + nC1 * a^(n-1) * b + nC2 * a^(n-2) * b^2 + ... + nCn * b^n, represents the binomial expansion of (a + b)^n.

1. In the rth term, the coefficient is nCr, which represents the number of ways to choose r elements from a set of n elements.
2. The first term in the rth term of the expansion is a raised to the power of (n - r).
3. The second term is b raised to the power of r.

Therefore, the correct answer is c) nCr * a^(n - r) * b^r.