How to Approach This Limit Involving a Riemann Sum?

In summary, pointers are variables that store the memory address of another variable and allow us to manipulate the values at those memory addresses for solving a sum. To declare and initialize a pointer, an asterisk (*) and the variable name is used, and to initialize it, the ampersand (&) operator is used to assign the memory address of a variable. Multiple pointers can point to the same variable, meaning they will all have the same memory address and affect the value accessed through them. To use pointers to solve a sum, a pointer is declared and initialized to point to the variables, and pointer arithmetic is used to manipulate the values without changing their original values. Common mistakes to watch out for when using pointers to solve a sum include not properly initializing
  • #1
oskar-
1
0
Hi all, perhaps someone can shed some light on the following sum:

[tex]
\lim_{m\rightarrow\infty}\frac{1}{m}\sum_{k=1}^{m-1}\left[1-\left(\frac{k}{2m-k}\right)^{1/2} \right]^2
[/tex]

What particularly throws me off is having the m variable as part of the summands. I have ran numerical simulations and it appears to "converge" to a constant as m grows large.

Any pointers to some theory that could help me solve this is greatly appreciated :)
 
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  • #2
That looks like a Riemann sum.
 

Related to How to Approach This Limit Involving a Riemann Sum?

1. What are pointers and how do they help with solving a sum?

Pointers are variables that store the memory address of another variable. They help with solving a sum by allowing us to manipulate the values at those memory addresses instead of directly manipulating the original variables.

2. How do I declare and initialize pointers?

To declare and initialize a pointer, you use an asterisk (*) followed by the variable name. For example, "int *ptr" declares a pointer named ptr that points to an integer. To initialize it, you assign the memory address of a variable to the pointer using the ampersand (&) operator. For example, "ptr = &num" assigns the memory address of the integer variable num to the pointer.

3. Can I have multiple pointers pointing to the same variable?

Yes, you can have multiple pointers pointing to the same variable. This means that all the pointers will have the same memory address stored and will point to the same value. Any changes made to the value through one pointer will also affect the value accessed through the other pointers.

4. How do I use pointers to solve a sum?

To use pointers to solve a sum, you first declare and initialize a pointer to point to the variables involved in the sum. Then, you can use pointer arithmetic to manipulate the values at those memory addresses. This allows you to perform operations on the original variables without actually changing their values.

5. Are there any common mistakes to watch out for when using pointers to solve a sum?

One common mistake when using pointers to solve a sum is not properly initializing the pointer. If the pointer is not initialized with a valid memory address, it can lead to unexpected results or errors. Another mistake is using the wrong data type for the pointer, which can also cause errors. It's important to double check the data types and memory addresses when using pointers to solve a sum.

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