# Solving Finite Series with Real Y

In summary, the conversation discusses a problem with finding the sum of a finite series involving sine functions and absolute values. One suggestion is to express sine with a complex exponential and use a geometric series. Another suggestion is to split the terms into positive and negative sets and sum them separately. However, this approach may be difficult due to the unpredictability of which terms should be positive or negative.
I cannot figure out the sum of this finite series:
|ysin(x)|+|y2sin(2x)|+...+|ynsin(nx)|
where y is real.
so I want to listen any opinion may help me>

Maybe try to express Sine with a complex exponential. Then you get a geometric series. This should work.

I had tried but it doesnot work it works just when there are no absolute values

Be creative ;) It works if you work through the cases, i.e. use logic to split positive and negative terms. It's messy, but gives you a closed form equation in the end.

thanks but I am not sure what you mean

I realize it's harder than I thought first.
I meant first determine which terms are going to be negative and which ones are positive (before the modulus).
Then sum both sets separately, because knowing the sign you can actually remove the modulus and replace it by *(-1) wherever you determined the sign to be negative. Depending on x you will have some runs of positive only terms and some negative only terms.
If x is a rational part of pi then it should be predictable. I haven't completely the calculation though...

I think it is so hard to do that in this manner because it is so hard to predict which terms should be positive or negative

At least for x=rational*pi it's fairly easy. But haven't put more thought in it.

## 1. What are finite series with real Y?

Finite series with real Y refer to mathematical series that have a finite number of terms and involve real numbers as variables or coefficients.

## 2. How do you solve finite series with real Y?

The most common method for solving finite series with real Y is by using the formula for the sum of a finite geometric series. This formula is Sn = a(1-r^n)/(1-r), where a is the first term, r is the common ratio, and n is the number of terms in the series.

## 3. What is the difference between solving finite series with real Y and infinite series?

The main difference is that finite series have a set number of terms, while infinite series have an infinite number of terms. This means that the sum of a finite series can be calculated, while the sum of an infinite series is typically represented by a limit.

## 4. Can finite series with real Y be used in real-life applications?

Yes, finite series with real Y are commonly used in real-life applications such as finance, physics, and engineering. They can be used to model growth, decay, and other real-world phenomena.

## 5. Are there any alternative methods for solving finite series with real Y?

Yes, besides the formula for the sum of a finite geometric series, there are also other methods such as using a table or graphing the series to find patterns and make predictions. Additionally, software programs and calculators can also be used to solve finite series with real Y.

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