Find the value of the following expression and round to the nearest integer: sum_(n=0)^(98)300(0.96)^(n-1) Answer:

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Find the value of the following expression and round to the nearest integer:  sum_(n=0)^(98)300(0.96)^(n-1) Answer:

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Find First Term: We are given a geometric series with the first term a = 300(0.96)^(-1) and the common ratio r = 0.96. 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 first term a. a = 300(0.96)^(-1) = 300 / 0.96 = 312.5Calculate Number of Terms: Next, we calculate the number of terms in the series. Since the series starts from n=0 and goes to n=98, there are 99 terms in total.Use Sum Formula: Now we can use the sum formula for a geometric series to find the sum S_99. S_99 = a(1 - r^n) / (1 - r) = 312.5(1 - 0.96^99) / (1 - 0.96)Calculate Numerator: We calculate the numerator of the fraction, which is 1 - 0.96^99. 1 - 0.96^99 ≈ 1 - a very small number Since 0.96^99 is a very small number, we can approximate this to 1 for the purpose of simplification.Calculate Denominator: Now we calculate the denominator of the fraction, which is 1 - 0.96. 1 - 0.96 = 0.04Find Sum: We can now find the sum S_99 by dividing the numerator by the denominator. S_99 ≈ 312.5 / 0.04 = 312.5 * 25 = 7812.5Round to Nearest Integer: Finally, we round the sum to the nearest integer. 7812.5 rounded to the nearest integer is 7813.

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=0}^{98} 300(0.96)^{n-1}$ $\newline$ Answer:

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Find the value of the following expression and round to the nearest integer:\newline∑n=098300(0.96)n−1 \sum_{n=0}^{98} 300(0.96)^{n-1} n=0∑98​300(0.96)n−1\newlineAnswer:

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=0}^{98} 300(0.96)^{n-1}$ $\newline$ Answer: