What function should I use for comparison

In summary, the conversation discusses how to compare a given series, ln(k)/k^2, with another series in order to determine if it converges or diverges. The individual is unsure of how to compare due to the presence of ln(k) in the numerator. They are advised to first determine if they believe the series converges or diverges and then find a suitable series to compare it with. A hint is given that k^(1/2) > ln(k) for all k. The individual eventually determines that if the series is 1/ln(k), they must first decide if it converges or diverges and then find a suitable series to compare it with.
  • #1
armolinasf
196
0

Homework Statement



If i have the series ln(k)/k^2 would I compare it to 1/k^2? The reason why I'm confused is that ln(k)/k^2 > 1/k^2 so if its greater than a function that converges it doesn't tell us anything right? So I'm not sure what exactly to compare it with on account of the ln(k) in the numerator. thanks for the help.
 
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  • #2
hello,

you are right that 1/k^2 will not help us in this case.

the first thing you need to decide is whether you think your series converges or diverges; that will determine the kind of series you want to compare it to. what do you think?
 
  • #3
my guess would be that it converges
 
  • #4
ok, then we need a series that converges, but that is bigger than ours.

do you have to use the comparison test, or can yo use any method?
 
  • #5
what series have you tried?
 
  • #6
Here's a hint: k^(1/2) > ln(k) for all k.
 
  • #7
Alright if k^1/2 is greater than ln k i could compare it with K^(1/2)/k^2 = 1/k^3/2 which converges since p>1.

One more question: what if it were 1/ln(k)?
 
  • #8
good!

well, for 1/ln(k) we again first need to decide if we think it converges or diverges. this one should be pretty easy if we think carefully. if we think it diverges (and hopefully we do :smile:), we need f(k) > ln(k) and 1/f(k) divergent. that shouldn't be too hard to find.

cheers
 

1. What is the best function to use for numerical comparison?

The best function to use for numerical comparison would depend on the specific programming language or software being used. Some common functions for numerical comparison include "equals" (==), "greater than" (>), "less than" (<), and "not equals" (!=). It is important to check the documentation or do some research to determine the most appropriate function for your specific needs.

2. Can I use the same function for comparing strings and numbers?

No, strings and numbers are different data types and therefore require different functions for comparison. For strings, you may use functions such as "equals" (==), "not equals" (!=), or "contains" (e.g. in JavaScript). For numbers, you may use functions such as "greater than" (>), "less than" (<), or "equal to" (===).

3. What function should I use for case-insensitive comparison?

For case-insensitive comparison of strings, you may use functions such as "equalsIgnoreCase" (in Java) or "toLowerCase" (in JavaScript) to convert both strings to lowercase before using an "equals" function. Some languages may also have a specific function for case-insensitive comparison, so it is important to check the documentation or do some research.

4. How do I compare objects or arrays?

Objects and arrays are complex data types and cannot be compared using simple functions. You may need to use specific methods or functions to compare objects or arrays, depending on the programming language or software being used. Some common methods include "isEqual" (in JavaScript) or "equals" (in Java). It is important to check the documentation or do some research to determine the best method for comparing objects or arrays.

5. Can I use if/else statements for comparison instead of a function?

Yes, you can use if/else statements for comparison instead of a function. However, using a function may be more efficient and easier to read and maintain. It is also important to consider that if/else statements may not cover all possible comparison scenarios, so using a function specifically designed for comparison may be a better option.

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