Here's a C++ program that reads a text file containing a list of numbers and finds the largest sum of any non-adjacent numbers in the list:

```cpp
#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>

int findLargestNonAdjacentSum(const std::vector<int>& nums) {
    int incl = nums[0];
    int excl = 0;
    int excl_new;

    for (size_t i = 1; i < nums.size(); ++i) {
        excl_new = std::max(incl, excl);
        incl = excl + nums[i];
        excl = excl_new;
    }

    return std::max(incl, excl);
}

int main() {
    std::string filename;
    std::cout << "Enter the name of the input file: ";
    std::cin >> filename;

    std::ifstream inputFile(filename);

    if (!inputFile.is_open()) {
        std::cerr << "Error opening the file." << std::endl;
        return 1;
    }

    std::vector<int> numbers;
    int num;

    while (inputFile >> num) {
        numbers.push_back(num);
    }

    inputFile.close();

    int largestSum = findLargestNonAdjacentSum(numbers);
    std::cout << "The largest sum of non-adjacent numbers is: " << largestSum << std::endl;

    return 0;
}
```

To use this program, create a text file with one number per line. Then compile and run the program, providing the name of the text file when prompted.

For example, given a text file named `numbers.txt` with the following content:

```
2
4
6
2
5
```

The output will be:

```
Enter the name of the input file: numbers.txt
The largest sum of non-adjacent numbers is: 13
```
Develop a C++ program that reads a text file containing a list of numbers, one per line, and finds the largest sum of any non-adjacent numbers in the list. For example, given the list [2, 4, 6, 2, 5], the largest sum would be 13 (2 + 6 + 5).
