there are 15 terms in the expansion of the binomial (a+b)^n. determine the value of n.
please explain to me how to come about this!
thanks!
(a+b)^1 has 2 terms
(a+b)^2 has 3 terms
....
(a+b)^15 has ----- terms.
To determine the value of n in the expansion of the binomial (a+b)^n, we need to use the binomial theorem. The binomial theorem states that the expansion of (a+b)^n will have (n+1) terms.
In this case, you are given that there are 15 terms in the expansion. Therefore, we can set up the equation:
n + 1 = 15
To find the value of n, we subtract 1 from both sides of the equation:
n = 15 - 1
Thus, n = 14.
So, the value of n is 14.
To summarize the steps:
1. Use the binomial theorem, which states that the expansion of (a+b)^n will have (n+1) terms.
2. Set up the equation: n + 1 = 15.
3. Solve for n by subtracting 1 from both sides of the equation.
4. Therefore, n = 14.