Calculate sum of row but its initial row number and row count - google-sheets

Question

Let's say I have a column of numbers:
1
2
3
4
5
6
7
8
Is there a formula that can calculate sum of numbers starting from n-th row and adding to the sum k numbers, for example start from 4th row and add 3 numbers down the row, i.e. PartialSum(4, 3) would be 4 + 5 + 6 = 15
BTW I can't use App Script as now it has some type of error Error code RESOURCE_EXHAUSTED. and in general I have had issue of stabile work with App Script before too.

Answer 1

As Tanaike mentioned, the error code when using Google Apps Script was just a temporary bug that seems to be solved at this moment.
Now, I can think of 2 possible solutions for this using custom functions:
Solution 1
If your data follows a specific numeric order one by one just like the example provided in the post, you may want to consider using the following code:
function PartialSum(n, k) {
let sum = n;
for(let i=1; i<k; i++)
{
sum = sum + n + i;
}
return sum;
}
Solution 2
If your data does not follow any particular order and you just want to sum a specific number of rows that follow the row you select, then you can use:
function PartialSum(n, k) {
let ss = SpreadsheetApp.getActiveSheet();
let r = ss.getRange(n, 1); // Set column 1 as default (change it as needed)
let sum = n;
for(let i=1; i<k; i++)
{
let val = ss.getRange(n + i, 1).getValue();
sum = sum + val;
}
return sum;
}
Result:
References:
Custom Functions in Google Sheets

Answer 2

Formula:
= SUM( OFFSEET( initialCellName, 0, 0, numberOfElementsInColumn, 0) )
Example add 7 elements starting from A5 cell:
= SUM( OFFSEET( A5, 0, 0, 7, 0) )