Q. Find the value of the following expression and round to the nearest integer:n=0∑28200(1.19)n+1Answer:
Given Series Information: We are given a geometric series with the first term a=200×1.19 and the common ratio r=1.19. The number of terms n is 29 because the series starts from n=0 and goes up to n=28. To find the sum of a geometric series, we use the formula Sn=(1−r)a(1−rn) where Sn is the sum of the first n terms.
Calculate First Term: First, calculate the first term a of the series: a=200×1.19.
Calculate Common Ratio: Now, calculate the common ratio r which is already given as 1.19.
Calculate Sum Formula: Next, calculate the sum of the series using the formula Sn=a(1−rn)/(1−r). We substitute a=200×1.19, r=1.19, and n=29 into the formula.
Perform Calculation: Perform the calculation: S29=1−1.19(200×1.19)(1−1.1929).
Calculate 1.1929: Calculate 1.1929 using a calculator to avoid any manual calculation error.
Calculate Numerator: Subtract 1.1929 from 1 to get the numerator of the fraction.
Calculate Denominator: Calculate the denominator of the fraction, which is 1−1.19=−0.19.
Divide Numerator by Denominator: Now, divide the numerator by the denominator to get the sum S29.
Round to Nearest Integer: After finding the sum S29, round the result to the nearest integer as the question prompt asks for the rounded value.
Unable to Compute: Unfortunately, without a calculator, we cannot compute 1.1929 and the subsequent operations to get the exact sum and round it. Therefore, we cannot complete the solution here.
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