SUMMATION NOTATION
Under this section we require to do a brief review of summation notation or sigma notation. We will start out with two integers, n and m, along with n < m and a list of numbers denoted as given here,
an, an+1, an+2,..............,am-2, am-1, am
We need to add them up, or say as,
an + an+1 + an+2+...........+am-2 + am-1 + am
For large lists it can be a fairly cumbersome notation therefore we establish summation notation to denote these types of sums. The case above is denoted as given here.
aI = an + an+1 + an+2+...........+am-2 + am-1 + am
The i is termed as the index of summation. This notation gives us to add all the ai's up for all integers starting at n and ending on m.
For illustration,
i/(i+1) = (0/(0 +1)) + (1/(1 + 1)) + (2/(2 + 1)) + (3/(3 + 1)) + (4/(4 + 1)) = 163/60 = 2.71667¯
2i x2i+1 = 24 x9 + 25 x11 + 26 x13 = 16 x9 + 32 x11 + 64 x13
f(xi*) = f(x1*) + f(x2*) + f(x3*) = f(x4*)