Homework SourseSimplify the alternating sum using the Binomial TheoremSolut
Simplify the alternating sum using the Binomial Theorem
Solution
Note that
(a + b)^n = Sum [C(n, r) a^r b^(n - r)]
If we set
a = -3, b = 1,
(-3 + 1)^n = Sum [C(n, r) (-3)^r 1^(n - r)]
(-2)^n = Sum [C(n, r) (-3)^r]
Thus,
Sum[(-3)^r C(n, r)] = (-2)n [ANSWER]
![Simplify the alternating sum using the Binomial TheoremSolutionNote that (a + b)^n = Sum [C(n, r) a^r b^(n - r)] If we set a = -3, b = 1, (-3 + 1)^n = Sum [C(n,](/WebImages/28/simplify-the-alternating-sum-using-the-binomial-theoremsolut-1075207-1761563814-0.webp "Simplify the alternating sum using the Binomial TheoremSolutionNote that (a + b)^n = Sum [C(n, r) a^r b^(n - r)] If we set a = -3, b = 1, (-3 + 1)^n = Sum [C(n,")
