- #36
assyrian_77
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- 0
First of all, [itex]\sum_{j=0}^{\infty}(-1)^{j}x^{2j} \neq x^{2} + x^{4} + x^{6} + x^{8}[/itex], it is [itex]\sum_{j=0}^{\infty}(-1)^{j}x^{2j}=1-x^{2} + x^{4} - x^{6} + x^{8}...[/itex].
Thenarildno said:No. You MUST learn to read properly and stop writing sloppy and nonsensical maths.
We have:
[tex](-1)^{n}x^{2n}\sum_{j=0}^{\infty}=\frac{(-1)^{n}x^{2n}}{1+x^{2}}[/tex]
arildno said:We have:
[tex](-1)^{n}x^{2n}\sum_{j=0}^{\infty}=\frac{(-1)^{n}x^{2n}}{1+x^{2}}[/tex]
You're right, it doesn't I'll fix it right away.assyrian_77 said:Sorry arildno, but that doesn't make sense.
An urgent geometric series is a type of mathematical series in which each term is multiplied by a constant ratio in order to obtain the next term. The term "urgent" refers to the fact that the series must be solved quickly or immediately due to its importance or relevance in a particular problem or situation.
To find the sum of an urgent geometric series, you can use the formula S = a(1-r^n)/(1-r), where S is the sum, a is the first term, r is the common ratio, and n is the number of terms. Alternatively, you can also use the formula S = a(1-r)/(1-r), where a is the first term and r is the common ratio, if the series has an infinite number of terms.
The common ratio in an urgent geometric series is the constant number that is multiplied to each term in order to obtain the next term. It is denoted by the letter "r" and is usually a decimal or fraction. For example, in the series 2, 4, 8, 16, 32, the common ratio is 2 because each term is multiplied by 2 to get the next term.
An urgent geometric series can be applied in various real-life scenarios, such as compound interest calculations, population growth, and radioactive decay. It is also commonly used in business and finance, particularly in analyzing the growth or decline of investments or assets over time.
A finite urgent geometric series has a specific number of terms, while an infinite urgent geometric series has an unlimited number of terms. This means that the sum of a finite series can be calculated using a specific formula, whereas the sum of an infinite series can only be approximated using a formula or through other mathematical methods.