Find the value of the following expression and round to the nearest integer: sum_(n=1)^(20)600(0.91)^(n+1) Answer:

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Find the value of the following expression and round to the nearest integer:  sum_(n=1)^(20)600(0.91)^(n+1) Answer:

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Recognize Problem Type: Recognize that the given expression is a geometric series where the first term a1 is 600(0.91)^2, the common ratio r is 0.91, and the number of terms n is 20.Use Geometric Series Formula: Use the formula for the sum of a finite geometric series, which is S_n = a1(1 - r^n) / (1 - r), where S_n is the sum of the first n terms.Calculate First Term: Calculate the first term a1 by substituting n=1 into the expression, which gives us a1 = 600(0.91)^2. a1 = 600 * (0.91)^2 a1 = 600 * 0.8281 a1 = 496.86Calculate Sum S_20: Calculate the sum S_20 using the formula from Step 2 with a1 = 496.86, r = 0.91, and n = 20. S_20 = 496.86 * (1 - (0.91)^20) / (1 - 0.91)Calculate (0.91)^20: Calculate (0.91)^20 to find the value that will be subtracted from 1 in the numerator of the sum formula. (0.91)^20 ≈ 0.151356Substitute Value: Substitute the value from Step 5 into the sum formula to calculate S_20. S_20 = 496.86 * (1 - 0.151356) / (1 - 0.91) S_20 = 496.86 * (0.848644) / 0.09Perform Calculations: Perform the calculations to find the sum S_20. S_20 = 496.86 * 0.848644 / 0.09 S_20 = 421.788 / 0.09 S_20 = 4686.53333333Round to Nearest Integer: Round the sum S_20 to the nearest integer. S_20 ≈ 4687

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=1}^{20} 600(0.91)^{n+1}$ $\newline$ Answer:

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Find the value of the following expression and round to the nearest integer:\newline∑n=120600(0.91)n+1 \sum_{n=1}^{20} 600(0.91)^{n+1} n=1∑20​600(0.91)n+1\newlineAnswer:

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=1}^{20} 600(0.91)^{n+1}$ $\newline$ Answer: