[A-SSE4] (Alabama) series.) Present and defend the Example: Calculate mortgage payments. derivation of the formula for the sum of a finite geometric series. One approach: S = a + ar + ar2 + ar3 + . . . + arn rS = ar + ar2 + ar3 + . . . + arn+1 rS - S = arn+1 - a = a(rn+1 - 1) S = a(rn+1 - 1)/(r - 1), Recognize geometric series which exist in problem situations and use the sum formula to simplify and solve problems. 13 E.2.e 13.) (+) Know and apply the Binomial Theorem for the expansion of (x + in Students: 628-644 y)n powers of and for a positive integer where and are any numbers, with x y n, x y coefficients determined, for example, by Pascal's Triangle. (The Binomial Theorem Expand for sequential (x + y)n can be proved by mathematical induction or by a combinatorial argument.) [A-APR5] cases n = 1,2,3... that indicate a pattern, note the regularity in the pattern of exponents and coefficients, and generalize the expansion to the Binomial Theorem by connecting the pattern of Pascal's Triangle to the pattern of coefficients in the binomial expansion. Use the patterns present in the Binomial Theorem to expand binomials and identify coefficients of particular terms.
series.) [A-SSE4] (Alabama) Example: Calculate mortgage payments. Present and defend the derivation of the formula for the sum of a finite geometric series. One approach: S = a + ar + ar2 + ar3 + . . . + arn rS = ar + ar2 + ar3 + . . . + arn+1 rS - S = arn+1 - a = a(rn+1 - 1) S = a(rn+1 - 1)/(r - 1), Recognize geometric series which exist in problem situations and use the sum formula to simplify and solve problems. 13 E.2.e 13.) (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined, for example, by Pascal's Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.) [A-APR5] Students: Expand (x + y)n for sequential cases n = 1,2,3... that indicate a pattern, note the regularity in the pattern of exponents and coefficients, and generalize the expansion to the Binomial Theorem by connecting the pattern of Pascal's Triangle to the pattern of coefficients in the binomial expansion. Use the patterns present in the Binomial Theorem to expand binomials and identify coefficients of particular terms. 628-644