i need to find the upper bound of this: or the tight bound:

问题

lets say i have an expression:

(n)+((n-1)*2)+((n-2)*3)+((n-3)*4)+...+(3*(n-2))+(2*(n-1))+(1*(n))

what is the tight bound of this? or the upper bound? is this n^3? is this n^4? the maximum amount of number i can get out of this? thanks

EDIT: so: for i=1 then: the ans is 1.

i=2: (1*2 + 2*1) 1=3: (1*3 + 2*2 + 3*1) i=4: (1*4 + 2*3 + 3*2 + 4*1 )

and so on

回答1:

Try Wolfram Alpha ...

Sum[(i + 1) (n - i), {i, 0, n - 1}]

来源：https://stackoverflow.com/questions/4382014/i-need-to-find-the-upper-bound-of-this-or-the-tight-bound