Repeating Decimal Infinite Sum using Calculus Geometric Series | Summary and Q&A

TL;DR

This video explains how to find the sum of an infinite geometric series using the formula 1 divided by 1 minus the common ratio.

Key Insights

• 🥳 An infinite geometric series can be represented by adding infinitely many terms with a common ratio less than 1.
• 🥳 The sum of an infinite geometric series can be found using the formula 1 divided by 1 minus the common ratio.
• 🥳 The sum converges if the common ratio is less than 1, otherwise, it diverges.

Transcript

in this problem we have to find the sum of this infinite geometric series it's worth noting that this is something quite special this is actually the same thing as nine point nine bar right which is the same thing as nine point I mean if you remember at some point in our lives we learn that the bar means that the nines go on forever so it's really ... Read More

Questions & Answers

Q: How can you represent an infinite repeating decimal as an infinite geometric series?

An infinite repeating decimal can be represented as an infinite geometric series by breaking it up into individual terms and using the formula 1 divided by 1 minus the common ratio.

Q: What determines whether the sum of an infinite geometric series converges?

The sum converges if the common ratio of the series is less than 1. If it is equal to or greater than 1, the series diverges.

Q: Can you use the formula for finding the sum of an infinite geometric series for any repeating decimal?

Yes, you can use the formula for any repeating decimal by breaking it up into individual terms and applying the formula 1 divided by 1 minus the common ratio.

Q: How do you perform the division of decimals when finding the common ratio of an infinite geometric series?

You can convert decimals to fractions and then divide by the desired number. For example, 0.9 can be written as 9/10 and divided by 9 to get 1/10.

Summary & Key Takeaways

• An infinite geometric series is represented by adding up an infinite number of terms, each with a common ratio less than 1.

• To find the sum of an infinite geometric series, use the formula 1 divided by 1 minus the common ratio.

• This formula converges if the common ratio is less than 1.