- #1
beadmaster
- 7
- 0
Hi,
I can't think / remeber how to write the following expresion in a closed form,
the function is a summation of natural numbers between 1 and an upper limit "K", written as
Sigma x with limits K and 1 effectivly, straightforward etc...
what i want is the summation of all the "summations" between K and 1 so sigma (1,K) + sigma (1,(K-1)) + sigma (1,(K-2)) etc.. until it reaches sigma (1,1) ie 1.
its easy to visulise, take K as 5, the expression would be
5+4+3+2+1
+4+3+2+1
+3+2+1
+2+1
+1
which gives 35, i am wanting the answer in terms of K (im presuming its possible) or at least can be written much neater than an expansion, cheers (I thought it could possibly be written as a general sigma summation but prehaps with tending limits, but if so how do you represent the tending being discrete and not continous)
cheers,
tom
I can't think / remeber how to write the following expresion in a closed form,
the function is a summation of natural numbers between 1 and an upper limit "K", written as
Sigma x with limits K and 1 effectivly, straightforward etc...
what i want is the summation of all the "summations" between K and 1 so sigma (1,K) + sigma (1,(K-1)) + sigma (1,(K-2)) etc.. until it reaches sigma (1,1) ie 1.
its easy to visulise, take K as 5, the expression would be
5+4+3+2+1
+4+3+2+1
+3+2+1
+2+1
+1
which gives 35, i am wanting the answer in terms of K (im presuming its possible) or at least can be written much neater than an expansion, cheers (I thought it could possibly be written as a general sigma summation but prehaps with tending limits, but if so how do you represent the tending being discrete and not continous)
cheers,
tom