Summation without loops

Question

I have following double summation: ∑10,i=1 ∑i,j=1 (i^5/(10+j^i))

I am quite lost with this exercise, I tried the following code but I it returns an error although giving

Answer 1

You could expand all the possible i/j combinations and then sum up all the terms

i <- 1:10
ii <- rep(i, i)
jj <- unlist(sapply(i, function(x) seq(1,x)))
sum(ii^5/(10+jj^ii))
# [1] 20835.22