math - Calculating varied summation formula? -

i'm trying pragmatically emulate calculator's summation function without use of loops, reason why become expensive once function gets bloated. far, know of formula n(n+1)/2, works if function looks like:

from x = 1 100, Σ (x), result = 5050.

without loop, there way implement function where:

from x = 1 100, Σ (x^2+x)?

edit: note formula must account possible function bodies.

thanks answers

the formula Σ (x^2+x) equal Σ (x) + Σ (x^2). know how calculate Σ (x).

as Σ (x^2), known square pyramidal number. can see longer explanation here, formula is:

n³/3 + n²/2 + n/6

together, that's

n³/3 + n²/2 + n/6 + n(n+1)/2

or

(n³+2n)/3 + n²