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Find the sum of the infinite geometric series.\newline5+103+209+4027+…5 + \frac{10}{3} + \frac{20}{9} + \frac{40}{27} + \dots\newlineWrite your answer as an integer or a fraction in simplest form.\newline__\_\_

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Q. Find the sum of the infinite geometric series.\newline5+103+209+4027+…5 + \frac{10}{3} + \frac{20}{9} + \frac{40}{27} + \dots\newlineWrite your answer as an integer or a fraction in simplest form.\newline__\_\_
  1. Calculate Total Rolls: To solve this problem, we need to determine the number of rolls of tape the electrician should order to have at least 8,0008,000 centimeters of electrical tape. We are given that each roll contains 2,0002,000 centimeters of tape. We will use division to find out how many rolls are needed.\newlineCalculation: 8,000 cm8,000 \, \text{cm} (total tape needed) ÷2,000 cm\div 2,000 \, \text{cm} (tape per roll) =4= 4 rolls
  2. Verify Calculation: We check our calculation to ensure there are no mathematical errors. Since 2,000 cm2,000\,\text{cm} goes into 8,000 cm8,000\,\text{cm} exactly 44 times without any remainder, we can confirm that the electrician needs to order 44 rolls of tape.

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