Find the value of the following expression and round to the nearest integer: sum_(n=0)^(33)50(1.01)^(n) Answer:

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Find the value of the following expression and round to the nearest integer:  sum_(n=0)^(33)50(1.01)^(n) Answer:

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Given Geometric Series: We are given a geometric series with the first term a = 50 and the common ratio r = 1.01. 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. In this case, n = 34 because the series starts at n = 0 and goes up to n = 33.Calculate r^n: First, we calculate r^n, which is (1.01)^34. This is the common ratio raised to the power of the number of terms.Substitute values into formula: Using a calculator, we find that (1.01)^34 is approximately 1.3976. This is the value of the common ratio raised to the power of the number of terms.Simplify the expression: Now we can plug the values into the sum formula for a geometric series: S_n = a(1 - r^n) / (1 - r). Substituting the values, we get S_34 = 50(1 - 1.3976) / (1 - 1.01).Perform calculations: Simplifying the expression, we get S_34 = 50(1 - 1.3976) / (-0.01). This simplifies to S_34 = 50(-0.3976) / (-0.01).Round the final answer: Performing the calculations, we get S_34 = 50 * 39.76. This equals 1988.Finally, we round the result to the nearest integer. Since the decimal part is less than 0.5, we round down, so the final answer is 1988.

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=0}^{33} 50(1.01)^{n}$ $\newline$ Answer:

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Find the value of the following expression and round to the nearest integer:\newline∑n=03350(1.01)n \sum_{n=0}^{33} 50(1.01)^{n} n=0∑33​50(1.01)n\newlineAnswer:

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=0}^{33} 50(1.01)^{n}$ $\newline$ Answer: