Find the value of the following expression and round to the nearest integer: sum_(n=0)^(98)100(1.01)^(n) Answer:

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Find the value of the following expression and round to the nearest integer:  sum_(n=0)^(98)100(1.01)^(n) Answer:

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Recognize Given Expression: We recognize that the given expression is a geometric series with the first term a = 100 and the common ratio r = 1.01. The sum of a finite geometric series can be calculated using the formula S_n = a(1 - r^n) / (1 - r), where n is the number of terms.Determine Number of Terms: First, we need to determine the number of terms in the series. Since the series starts at n = 0 and goes up to n = 98, there are a total of 99 terms (we include the starting term).Plug Values into Formula: Now we can plug the values into the sum formula for a geometric series: S_n = 100(1 - 1.01^99) / (1 - 1.01).Calculate Power: We calculate the power 1.01^99 using a calculator to avoid any manual calculation error.Substitute Power into Formula: After calculating the power, we substitute it back into the formula: S_n = 100(1 - 1.01^99) / (1 - 1.01).Perform Subtraction: We perform the subtraction in the numerator and the denominator: S_n = 100(1 - 1.01^99) / (-0.01).Simplify Expression: We multiply the numerator and denominator by -100 to simplify the expression: S_n = -10000(1 - 1.01^99).Calculate Value: We calculate the value of the expression -10000(1 - 1.01^99) using a calculator to ensure accuracy.Round Result: Finally, we round the result to the nearest integer as the question prompt asks for the rounded value.

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=0}^{98} 100(1.01)^{n}$ $\newline$ Answer:

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Find the value of the following expression and round to the nearest integer:\newline∑n=098100(1.01)n \sum_{n=0}^{98} 100(1.01)^{n} n=0∑98​100(1.01)n\newlineAnswer:

Find the value of the following expression and round to the nearest integer: $\newline$ $\sum_{n=0}^{98} 100(1.01)^{n}$ $\newline$ Answer: