Q. Find the sum of the infinite geometric series.5+35+95+275+…Write your answer as an integer or a fraction in simplest form.__
Divide Total Amount: To solve this problem, we need to divide the total amount of electrical tape needed by the amount of tape on each roll.Calculation: 8,000cm÷2,000cm/roll
Calculate Number of Rolls: Evaluating the division gives us the number of rolls needed. 8,000cm÷2,000cm/roll=4rolls
Identify First Term and Ratio: First, identify the first term a and the common ratio r of the geometric series.The first term a is 5, and the common ratio r is 31, since each term is 31 of the previous term.
Find Sum Formula: The sum of an infinite geometric series can be found using the formula S=1−ra, where S is the sum, a is the first term, and r is the common ratio.Here, a=5 and r=31.
Substitute Values: Substitute the values of a and r into the formula to find the sum.S=(1−31)5
Calculate Denominator: Calculate the denominator of the fraction: 1−31=32.
Divide by Fraction: Now, divide the first term by the result from the previous step to find the sum of the series. S=325
Perform Multiplication: To divide by a fraction, multiply by its reciprocal.S=5×(23)
Perform Multiplication: To divide by a fraction, multiply by its reciprocal.S=5×(23)Perform the multiplication to find the sum.S=215 or 7.5However, since the question prompt asks for an integer or a fraction in simplest form, we leave the answer as a fraction.
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