Find the value of the following expression and round to the nearest integer: sum_(n=2)^(20)700(0.71)^(n-1) Answer:

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Find the value of the following expression and round to the nearest integer:  sum_(n=2)^(20)700(0.71)^(n-1) Answer:

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Given series parameters: We are given a geometric series with the first term a = 700(0.71)^(2-1) = 700(0.71) and the common ratio r = 0.71. The sum of a finite geometric series is given by the formula S_n = a(1 - r^n) / (1 - r), where n is the number of terms. First, we need to find the number of terms in the series.Calculate number of terms: The series starts at n=2 and ends at n=20, so the number of terms is 20 - 2 + 1 = 19. Now we can use the formula for the sum of a geometric series to find the sum.Calculate sum formula: Plugging the values into the formula, we get S_19 = 700(0.71)(1 - 0.71^19) / (1 - 0.71). Let's calculate the sum.Calculate common ratio: First, calculate 0.71^19 using a calculator to ensure accuracy. 0.71^19 ≈ 0.0059 (rounded to four decimal places for simplicity).Substitute values into formula: Now, substitute this value into the sum formula: S_19 ≈ 700(0.71)(1 - 0.0059) / (1 - 0.71).Calculate numerator subtraction: Perform the subtraction in the numerator: 1 - 0.0059 = 0.9941.Calculate denominator subtraction: Now, perform the subtraction in the denominator: 1 - 0.71 = 0.29.Calculate numerator multiplication: Multiply the numerator: 700 * 0.71 * 0.9941 ≈ 494.287.Calculate division: Divide by the denominator: 494.287 / 0.29 ≈ 1704.438.Round final result: Round the result to the nearest integer: 1704.438 rounds to 1704.

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=2}^{20} 700(0.71)^{n-1}$ $\newline$ Answer:

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Find the value of the following expression and round to the nearest integer:\newline∑n=220700(0.71)n−1 \sum_{n=2}^{20} 700(0.71)^{n-1} n=2∑20​700(0.71)n−1\newlineAnswer:

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=2}^{20} 700(0.71)^{n-1}$ $\newline$ Answer: