AfterSunShine said:Homework Statement
Find [tex]a_n[/tex] & [tex]b_n[/tex] such that [tex]\sum_{n=0}^{\infty}a_n[/tex] & [tex]\sum_{n=0}^{\infty}b_n[/tex] are convergent series, but [tex]\displaystyle \sum_{n=0}^{\infty} \left( \sqrt{a_n} \cdot b_n \right)[/tex] diverges.
Homework Equations
None.
The Attempt at a Solution
Try too hard for this but still cannot find such [tex]a_n[/tex] & [tex]b_n[/tex].
That is not so bad as a start. Can you modify the series in order to keep them converging, but doing so significantly slower?AfterSunShine said:basically I tried a_n = 1/n^2 & b_n = (-1)^n / n but failed
The variables a_n and b_n are often used to represent unknown coefficients or parameters in a mathematical model. By finding their values, scientists can better understand and predict the behavior of a system or phenomenon.
The techniques used to find a_n and b_n vary depending on the specific problem being studied. Some common methods include regression analysis, numerical optimization, and curve fitting. Scientists may also use computer simulations or mathematical models to determine the values of these variables.
The values of a_n and b_n can greatly impact the results of a scientific study. These variables often represent important factors that influence the behavior of a system or phenomenon. By accurately determining their values, scientists can make more accurate predictions and draw more meaningful conclusions from their research.
Yes, a_n and b_n can take on any real or complex values depending on the context of the study. In some cases, negative or complex values may be necessary to accurately represent the behavior of a system or phenomenon.
While a_n and b_n can be useful variables in many scientific studies, they also have limitations. These values may only be applicable in certain conditions or may not fully capture all aspects of a complex system. Additionally, the process of finding a_n and b_n may be subject to error, which can impact the accuracy of the study's results.