. Give the first three terms of (1 + x)15 in ascending order
Question
. Give the first three terms of (1 + x)15 in ascending order
Solution
The first three terms of the binomial expansion of (1 + x)^15 in ascending order can be found using the binomial theorem, which states that:
(a + b)^n = Σ (n choose k) * a^(n-k) * b^k
where "n choose k" is a binomial coefficient.
For (1 + x)^15, a = 1, b = x, and n = 15.
The first term (k = 0) is:
(15 choose 0) * 1^(15-0) * x^0 = 1
The second term (k = 1) is:
(15 choose 1) * 1^(15-1) * x^1 = 15x
The third term (k = 2) is:
(15 choose 2) * 1^(15-2) * x^2 = 105x^2
So, the first three terms of (1 + x)^15 in ascending order are 1, 15x, and 105x^2.
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