Find the value of the following expression and round to the nearest integer: sum_(n=2)^(25)900(1.21)^(n-1) Answer:

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Find the value of the following expression and round to the nearest integer:  sum_(n=2)^(25)900(1.21)^(n-1) Answer:

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Recognize Given Expression: Recognize that the given expression is a geometric series where the first term a = 900(1.21)^(2-1) = 900(1.21), the common ratio r = 1.21, and the number of terms n = 25 - 2 + 1 = 24.Use Formula for Sum: Use the formula for the sum of a finite geometric series, which is S_n = a(1 - r^n) / (1 - r), where S_n is the sum of the first n terms of the geometric series.Plug Values into Formula: Plug the values into the formula: S_24 = 900(1.21)(1 - 1.21^24) / (1 - 1.21).Calculate Numerator: Calculate the numerator of the fraction: 1 - 1.21^24. This requires calculating 1.21^24 first. 1.21^24 ≈ 799.53 (using a calculator) Now, subtract this from 1: 1 - 799.53 ≈ -798.53.Calculate Denominator: Calculate the denominator of the fraction: 1 - 1.21 = -0.21.Divide Numerator by Denominator: Now, divide the numerator by the denominator: -798.53 / -0.21 ≈ 3802.52.Multiply by First Term: Multiply this result by the first term of the series (900 * 1.21) to get the sum of the series: 3802.52 * 900 * 1.21 ≈ 4142712.12.Round to Nearest Integer: Round the result to the nearest integer: 4142712.12 rounds to 4142712.

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=2}^{25} 900(1.21)^{n-1}$ $\newline$ Answer:

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Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=2}^{25} 900(1.21)^{n-1}$ $\newline$ Answer: