- #1
Werg22
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Is this true?
f(x)=sin(x)=x(x-2pi)(x-4pi)(x-6pi)...
edit:
f(x)=sin(x)=x(x-pi)(x-2pi)(x-3pi)(x-4pi)...
f(x)=sin(x)=x(x-2pi)(x-4pi)(x-6pi)...
edit:
f(x)=sin(x)=x(x-pi)(x-2pi)(x-3pi)(x-4pi)...
Last edited:
I was trying to point out that sin(pi) = 0 but your serie would never go to 0.Werg22 said:I'm affraid I do not see what you mean... the serie is infinite...
Werg22 said:Sorry what I really meant is f(x)=sin(x)=x(x-pi)(x-2pi)(x-3pi)(x-4pi)...
Really sorry.
The concept of infinite product is both true and a mathematical abstraction. In mathematics, an infinite product represents the result of multiplying an infinite number of factors together. However, in reality, it is impossible to have an actual infinite number of factors. Therefore, the concept of infinite product is often used as a tool for mathematical analysis and is not always applicable to real-world scenarios.
Yes, an infinite product can sometimes equal a finite number. This can only occur if the infinite product converges to a limit. In other words, if the value of the product approaches a finite number as the number of factors increases without bound, then it can be considered equal to that finite number.
No, an infinite product is not always divergent. The convergence or divergence of an infinite product depends on the value of its individual factors. If the factors decrease in value at a fast enough rate, the product may converge to a finite number. However, if the factors increase in value or do not decrease fast enough, the product will diverge.
Yes, an infinite product can have a negative value. This can occur if the factors alternate between positive and negative values, resulting in the overall product being negative. However, if the factors are all positive or all negative, the product will also be positive.
The concept of infinite product has several real-world applications, such as in finance and economics, where it is used to model compound interest or exponential growth. It is also used in physics and engineering to represent infinite series and to approximate functions. In computer science, infinite products are used in algorithms and data compression techniques.