Find the value of the following expression and round to the nearest integer: sum_(n=2)^(50)50(1.12)^(n-2) Answer:

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Find the value of the following expression and round to the nearest integer:  sum_(n=2)^(50)50(1.12)^(n-2) Answer:

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Recognize Geometric Series: Recognize that the given expression is a geometric series. A geometric series has the form sum_(n=0)^(N) ar^n, where a is the first term, r is the common ratio, and N is the number of terms. In this case, the first term is 50(1.12)^0 = 50, the common ratio r is 1.12, and the series starts at n=2 and goes to n=50.Adjust Series Starting Point: Adjust the series to start at n=0 for easier calculation. To do this, we can factor out the term (1.12)^2 from each term in the series, which gives us 50(1.12)^0 + 50(1.12)^1 + ... + 50(1.12)^(48). Now the series starts at n=0 and goes to n=48.Use Finite Series Formula: Use the formula for the sum of a finite geometric series, which is S = a(1 - r^N) / (1 - r), where S is the sum of the series, a is the first term, r is the common ratio, and N is the number of terms. Here, a = 50, r = 1.12, and N = 49 (since we start at n=0 and go to n=48, which is 49 terms).Calculate Sum Formula: Plug the values into the formula to find the sum of the series. S = 50(1 - 1.12^49) / (1 - 1.12)Calculate 1.12^49: Calculate the sum using the values from Step 4. S = 50(1 - 1.12^49) / (1 - 1.12) S = 50(1 - 1.12^49) / (-0.12) S = -50(1 - 1.12^49) / 0.12Substitute Value in Formula: Calculate 1.12^49 using a calculator to ensure accuracy. 1.12^49 ≈ 289.68 (rounded to two decimal places for simplicity)Perform Multiplication and Division: Substitute the value from Step 6 into the sum formula. S = -50(1 - 289.68) / 0.12 S = -50(-288.68) / 0.12Find Final Sum: Perform the multiplication and division to find the sum. S = 50 * 288.68 / 0.12 S ≈ 50 * 2405.67 S ≈ 120283.33Round to Nearest Integer: Round the sum to the nearest integer. S ≈ 120283

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=2}^{50} 50(1.12)^{n-2}$ $\newline$ Answer:

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Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=2}^{50} 50(1.12)^{n-2}$ $\newline$ Answer: