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


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