Find the value of the following expression and round to the nearest integer: sum_(n=2)^(34)30(1.3)^(n-2) Answer:

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Find the value of the following expression and round to the nearest integer:  sum_(n=2)^(34)30(1.3)^(n-2) Answer:

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Given series and terms: We are given a geometric series with the first term a = 30(1.3)^(2-2) = 30(1) = 30 and a common ratio r = 1.3. The sum of a finite geometric series can be found using 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.Number of terms calculation: The series starts at n=2 and ends at n=34, so the number of terms is 34 - 2 + 1 = 33. Now we can use the formula for the sum of a geometric series.Formula for sum of geometric series: Plugging the values into the formula, we get S_33 = 30(1 - 1.3^33) / (1 - 1.3). We need to calculate 1.3^33 and then proceed with the formula.Calculate 1.3^33: Using a calculator, we find that 1.3^33 is approximately 1425.7631. Now we substitute this value into the formula.Substitute values into formula: Substituting the values, we get S_33 = 30(1 - 1425.7631) / (1 - 1.3) = 30(-1424.7631) / (-0.3). We simplify this to get the sum.Simplify expression for sum: Simplifying the expression, we get S_33 = 30 * 1424.7631 / 0.3. Performing the division and multiplication, we find the sum.Perform division and multiplication: The sum S_33 is approximately 30 * 4749.2103 = 142476.309. Now we round this to the nearest integer.Round sum to nearest integer: Rounding 142476.309 to the nearest integer, we get 142476.

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=2}^{34} 30(1.3)^{n-2}$ $\newline$ Answer:

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Find the value of the following expression and round to the nearest integer:\newline∑n=23430(1.3)n−2 \sum_{n=2}^{34} 30(1.3)^{n-2} n=2∑34​30(1.3)n−2\newlineAnswer:

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=2}^{34} 30(1.3)^{n-2}$ $\newline$ Answer: