# Bounds of summation

1. Sep 24, 2010

### smslca

can the lower bound of a summation(sigma) be any real number ?
i.e ex: sigma(LB:sqrt(2) or (9/2) etc )
Even a lower bound be a real number is possible or not can upper bound be any real number or is it a strict rule that '1' should be added to lower bound to get the consecutive number.?
i.e. ex: LB + sqrt(2) or (9/2) etc.

2. Sep 24, 2010

### Tac-Tics

You mean something like

$$\Sigma_{i=\pi}^{\pi^2}i$$

?

If so, no. In standard usage, the bounds are always integers.

Of course, you could always choose a different definition. Many variations on Σ exist, like the Mobius function, which sums over the divisors of an integer.

3. Sep 24, 2010

$$\sum_{j \text{ prime}} {\frac 1 j }$$
(or something similar). If you wanted the "jump" between successive terms in a sum to be $\sqrt 2$, and start at $\pi$, you might do something like this:
$$\sum_{j = 1}^n {(\pi + (j-1)\sqrt{2})}$$