Creating a for loop that takes a manual sum of squares within and between groups

Question

Per my lack of understanding of loops, I'm wondering how I might go about translating these two mathematical functions into R. Any help would be greatly appreciated!

My real confusion is more-so that I don't know how I might start coding a sum into R

Answer 1

Start by trying to understand this

a = 1:100
mysum = 0
for (i in seq_along(a)){
  mysum = a[i] + mysum 
}
mysum

This code sums the numbers from 1:100