What is the coefficient of the fifth term in the expansion of (x + 1)^8?
(Broken Link Removed)
Does that help?
If not, read this
http://en.wikipedia.org/wiki/Pascal%27s_triangle
not quite.
in this case
n=8
k=(x+1)
To find the coefficient of the fifth term in the expansion of (x + 1)^8, we can use the Binomial Theorem. The Binomial Theorem gives us a formula to expand any binomial expression raised to a power. The formula states that for a binomial (a + b)^n, the k-th term is given by:
T(k) = C(n, k) * (a^(n-k)) * (b^k)
where C(n, k) represents the binomial coefficient, and it is equal to n! / (k! * (n - k)!).
In the given expression (x + 1)^8, we want to find the coefficient of the fifth term, which corresponds to the term with k = 5.
Using the formula for the k-th term, we have:
T(5) = C(8, 5) * (x^(8-5)) * (1^5)
The binomial coefficient C(8, 5) can be calculated as:
C(8, 5) = 8! / (5! * (8 - 5)!)
Simplifying further, we get:
C(8, 5) = (8! / (5! * 3!)) = (8 * 7 * 6) / (3 * 2 * 1) = 56
Therefore, the coefficient of the fifth term in the expansion of (x + 1)^8 is 56.