smart_worker said:Homework Statement
Find the general term and test the nature of the series:
Homework Equations
1+1*4+1*4*7+...
The Attempt at a Solution
Term N = Term (N-1) * 3N-2
Hence,3(N-1)-2 * 3N-2
which simplifies to (3N-5)(3N-1) = 9N^2 - 18N + 5
Is this correct?
A general term of a series is a formula or expression that represents the pattern or rule for the terms in a series. It can be used to calculate any term in the series without having to write out all of the previous terms.
To find the general term of a series, you need to look for a pattern in the terms. This could be a common difference or ratio between the terms. Once you have identified the pattern, you can write out a formula or expression that represents it. You can then use this formula to calculate any term in the series.
Knowing the general term of a series can help you to quickly calculate any term in the series without having to write out all of the previous terms. It also allows you to identify the behavior and characteristics of the series, such as whether it is finite or infinite, convergent or divergent.
Some common types of series that have general terms include arithmetic series, geometric series, and power series. These series have specific formulas or expressions that can be used to calculate any term in the series.
The general term of a series can be used in many real-world applications, such as predicting future population growth, calculating compound interest, and modeling natural phenomena like population growth or radioactive decay. It can also be used in computer programming and data analysis to generate and analyze large sets of data.