Kurani said:Homework Statement
Find the limit n to Infinity of summation (i=1 to n) 1/n * ((i/n)^2)
The Attempt at a Solution
I thought it was zero at first because 1/n goes to zero but apparently that's not right. I also tried to convert to an integral and got integral of i^2/n^2 which equals i^3/3*n^2 but that's not right either.
A limit of summation is a mathematical concept that represents the value that a summation approaches as the number of terms in the summation approaches infinity.
To find the limit of a summation, you can use various techniques such as the squeeze theorem, the comparison test, or the ratio test. It is important to understand the properties of the series and the terms being added to determine the appropriate method to use.
When a limit of summation is infinite, it means that the sum of the terms in the series continues to increase without bound. This can happen when the terms being added become larger and larger, or when the number of terms in the series increases without a bound.
Yes, the limit of summation can be negative. This can occur when the terms being added are negative and the number of terms in the series is large enough to result in a negative sum.
Finding the limit of summation is important in understanding the behavior and convergence of infinite series. It allows us to determine if a series will approach a specific value or if it will continue to increase without bound. This can have applications in various fields such as physics, engineering, and economics.