I have this question:
Find an explicit expression, i.e. a simple fraction involving powers of n, for the following sum:
$\sum_{j=1}^n \sum_{k=j}^n k$
Setting n at 5, I can see that the notation gives the sum of numbers j to n on each run through, so like this:
j=1 gives $(1+2+3+4+5)$
j=2 gives $(2+3+4+5)$
j=3 gives $(3+4+5)$
j=4 gives $(4+5)$
j=5 gives $(5)$
However, this is as far as I can get before hitting a brick wall. I can't see how you'd get an expression involving powers of n to perform that same summation. Any help is VERY much appreciated; I'm remarkably new to this area of mathematics.