Partial sums: term value from partial sum | Series | AP Calculus BC | Khan Academy

TL;DR

The video explains how to find the seventh term in a series using the formula for the sum of the first n terms.

Transcript

• [Instructor] We're told that the nth partial sum of the series from n equals one to infinity of a sub n is given by. And so the sum of the first n terms is n squared plus one over n plus one. And they want us to figure out, what is the actual seventh term? And, like always, pause this video and see if you can figure it out on your own before we w... Read More

Key Insights

• 🍉 The sum of the first n terms in a series can be determined using the appropriate formula.
• 🍉 To find a specific term in a series, subtract the sum of the previous terms from the sum of all terms.
• 👻 Multiplying the numerator and denominator by the same value allows for the finding of the common denominator.

Questions & Answers

Q: How is the seventh term in a series found?

The seventh term in a series can be found by subtracting the sum of the first six terms from the sum of the first seven terms.

Q: What formula is used to calculate the sum of the first n terms in a series?

The formula for the sum of the first n terms in a series is given as n^2 + 1 / (n + 1).

Q: How do you find the common denominator when subtracting fractions?

To find the common denominator, you multiply the denominators of the fractions together. In this case, it is 56.

Q: How is the fraction simplified to 27/28?

By reducing the fraction 54/56, it can be simplified to 27/28, which is the value of the seventh term in the series.

Summary & Key Takeaways

• The video demonstrates how to find the seventh term in a series by subtracting the sum of the first six terms from the sum of the first seven terms.

• The formula used for the sum of the first n terms is given, allowing for the calculation of the desired term.

• By substituting the values into the formula, performing arithmetic calculations, and simplifying the fraction, the seventh term is determined to be 27/28.