To find the coefficient of x^3 in (1 + 14x)^6, we can use the binomial theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k = 0 to n.

In this case, a = 1, b = 14x, and n = 6. We want to find the coefficient of x^3, so we set k = 3.

The binomial coefficient (n choose k) = n! / [k!(n-k)!], where "!" denotes factorial.

So, the coefficient of x^3 is (6 choose 3) * 1^(6-3) * (14)^3.

= (6*5*4 / 3*2*1) * 1^3 * 14^3

= 20 * 1 * 2744

= 54880

So, the coefficient of x^3 in (1 + 14x)^6 is 54880. None of the options (a. 211, b. 316, c. 516, d. 1116) match this result.

Question

To find the coefficient of x^3 in (1 + 14x)^6, we can use the binomial theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k = 0 to n.

In this case, a = 1, b = 14x, and n = 6. We want to find the coefficient of x^3, so we set k = 3.

The binomial coefficient (n choose k) = n! / [k!(n-k)!], where "!" denotes factorial.

So, the coefficient of x^3 is (6 choose 3) * 1^(6-3) * (14)^3.

= (6*5*4 / 3*2*1) * 1^3 * 14^3

= 20 * 1 * 2744

= 54880

So, the coefficient of x^3 in (1 + 14x)^6 is 54880. None of the options (a. 211, b. 316, c. 516, d. 1116) match this result.

Knowee AI · Accepted Answer

To find the coefficient of x^3 in (1 + 14x)^6, we can use the binomial theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k = 0 to n.

In this case, a = 1, b = 14x, and n = 6. We want to find the coefficient of x^3, so we set k = 3.

The binomial coefficient (n choose k) = n! / [k!(n-k)!], where "!" denotes factorial.

So, the coefficient of x^3 is (6 choose 3) * 1^(6-3) * (14)^3.

= (6*5*4 / 3*2*1) * 1^3 * 14^3

= 20 * 1 * 2744

= 54880

So, the coefficient of x^3 in (1 + 14x)^6 is 54880. None of the options (a. 211, b. 316, c. 516, d. 1116) match this result.

Find the coefficient of 𝑥3 in (1 + 14 𝑥)6a. 211b. 316c. 516d. 1116

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