How to Solve a Limit Question for Series Objects | Step-by-Step Guide

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In summary, the conversation is about finding the limit of a series and using equations to solve it. The person also mentions adding the numbers to estimate the limit. The solution provided is \frac{1}{n} - \frac{1}{{n + 1}}i.
  • #1
transgalactic
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[SOLVED] limit question

i added a file with the question and how i tried to find the legality between the
objects of the series

lim [1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(n*(n+1))]
n>>infinity


i can't find the total sum of all the objects in the series

if i would get the total sum of all the objects
i can get the limit

i could add the first numbers and to make an estimation about the limit
but how i solve it in equetions??
 

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  • #2
Does this help?

[tex]\frac{1}{{n\left( {n + 1} \right)}} = \frac{1}{n} - \frac{1}{{n + 1}}[/tex]
 
  • #3
i got

lim 1- [1/(n-1)] =1
n>>infinity


thanks
 
Last edited:
  • #4
The limit is indeed 1.
 

FAQ: How to Solve a Limit Question for Series Objects | Step-by-Step Guide

What is a limit question for series objects?

A limit question for series objects involves finding the value that a series approaches as the number of terms increases towards infinity. It is used to determine the convergence or divergence of a series.

What are the steps to solve a limit question for series objects?

First, identify the given series and its terms. Then, use a convergence test (such as the ratio or root test) to determine if the series converges or diverges. If the series converges, use the limit comparison test to find the limit. If the series diverges, use the direct comparison test to determine if it diverges to positive or negative infinity.

How do I know which convergence test to use?

The choice of convergence test depends on the form of the series. For example, the ratio test is used for series with factorials or exponentials, while the root test is used for series with nth powers. It is important to try more than one test to confirm the convergence or divergence of a series.

Can I use a calculator to solve a limit question for series objects?

While a calculator can be used to evaluate the terms of a series, convergence tests and comparison tests must be done by hand. Additionally, a calculator may not always provide an accurate result for infinite series.

What is the importance of understanding how to solve limit questions for series objects?

Understanding how to solve limit questions for series objects is important in many areas of mathematics and science, as series are used to represent real-life phenomena, such as growth, decay, and oscillations. It also helps in determining the behavior and convergence of mathematical equations and expressions.

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