What is the sum of the series?

MHB
Thread starter ineedhelpnow
Start date Jul 29, 2014
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Series Sum

In summary, a series is a sequence of numbers added together in a specific order. To find the sum of a series, all the numbers in the series are added together to get a single value. This can be done using a formula, mathematical pattern, calculator, or computer program. Finding the sum of a series is significant in solving mathematical problems and understanding the behavior and patterns of a series. A series is convergent if the sum of its terms approaches a finite value, while it is divergent if the sum approaches infinity or does not have a finite value.

Jul 29, 2014

ineedhelpnow

$\sum_{n=0}^{\infty}\frac{2^n}{3^nn!}$

is this correct?

$\sum_{n=0}^{\infty}(\frac{2}{3})^n \frac{1}{n!}$

$\sum_{n=0}^{\infty}\frac{(x)^n}{n!}=e^x$

$x=2/3$

$e^x=e^{2/3}

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Jul 29, 2014

MarkFL

Gold Member

MHB

Yes, that's correct. :D

Related to What is the sum of the series?

What is a series?

A series is a sequence of numbers that are added together in a specific order.

What does it mean to find the sum of a series?

Finding the sum of a series means to add up all the numbers in the series to get a single value.

How do I find the sum of a series?

To find the sum of a series, you can use a formula or a mathematical pattern to add up all the numbers in the series. Alternatively, you can also use a calculator or write a computer program to find the sum.

What is the significance of finding the sum of a series?

Finding the sum of a series can help in solving mathematical problems, like calculating the total cost of multiple items or finding the average of a set of values. It can also help in understanding the general behavior and patterns of a series.

How do I know if a series is convergent or divergent?

A series is convergent if the sum of its terms approaches a finite value as the number of terms increases. On the other hand, a series is divergent if the sum of its terms approaches infinity or does not have a finite value.