What is the name of the math / calc function defined below:?

Question

f(x) = x + (x-1) + (x-2) + ... + 2 + 1 + 0

for example, f(6) = 6+5+4+3+2+1+0 = 21

Also, is there a way to model easily in excel?

Answer 1

This is an arithmetic series. It is arithmetic because each term (number) is a fixed amount less than (or more than) the previous term. The formula for the sum above is f(x) = x(x+1)/2. Not sure about the excel part.

Answer 2

let´s write n instead of x

f(n) = 1+2+3+....+ (n-1)+n This is the sum of an arithmetic progression

f(n) = n*(n+1)/2 so f(6) = 6*7/2 =21 and f(50) = 50*51/2=1275

Answer 3

a) The $2.50 to $3 in 3 years ought to intend 50centincrease/3yrs or 100centsincrease/6years(fromNOW); end result: $4, 6years from NOW. b) [3 -4] / (-a million -a million) ==> m(slope) is -a million/(-2) or a million/2. f(x) =(a million/2)x +3.5 regardless of the indisputable fact that (pt-slope style): y - 4 =(a million/2)(x - a million) ======= For both issues ?y/?x determines the slope of the linear function; the numerator ?y is the change contained in the depending variable; and ?x is the corresponding change contained in the self sufficient variable. One depending formula from this huge evaluation should be [very last state -initial state of depending variable]/[very last state self sufficient variable -initial state indep. var.] it really is only a skeleton education guide; you ought to flesh out the perception so that you'll personal all the awareness as your human being.

Answer 4

Triangular numbers.

n*(n+1)/2