Understanding U_n: An Explanation of the Concept

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U_n refers to a sequence of numbers represented as U1, U2, ..., Un, where each U_n is a specific number in that sequence. The discussion emphasizes understanding the sum of these numbers as a function of n, highlighting the importance of knowing the individual values to compute the total. Participants are encouraged to explore the relationship between the sum of the sequence and its preceding elements. A specific example is provided to illustrate how to derive values using a given formula. Overall, the conversation aims to clarify the concept of U_n and its application in mathematical functions.
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Could anyone explain what is meant by U_n
 
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It are just numbers. That is, U_1,...,U_n are just numbers. You need to figure out which numbers they are.
 
Hi synkk
The wording is probably confusing you.
First, did you do (a) ? do it if you didn't

Then, as micromass told you, Un is just a number, well, in this case, you are dealing with a sequence of numbers, U1, ... Un
You have a generic formula for their sum, which is a function of n, being the result of summing the n elements U1,...Un
so, if you subtract the sum of all the elements, U1,...Un-1, what are you left with ?
Hope this helps so that you continue alone

Cheers...
 
Another way of looking at (a): if you were told that f(n)= n^2+ 4n, how would you find f(n-1)?

Then (b), what is f(n)- f(n-1)?
 

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