The expression you provided:

$\sum \left( \frac{1}{\sqrt{n}} + \frac{1}{\sqrt{n+1}} \right)$

is a summation of terms of the form:

$\frac{1}{\sqrt{n}} + \frac{1}{\sqrt{n+1}}$

This summation does not specify the limits, so I will assume that you want to perform this summation for values of $n$ from a starting point $n = 1$ to some upper limit, say $n = N$. In this case, the sum would be:

$\sum_{n=1}^{N} \left( \frac{1}{\sqrt{n}} + \frac{1}{\sqrt{n+1}} \right)$

If this assumption is correct, I can calculate it for any value of $N$, or provide a more generalized formula.

Let me know how you'd like to proceed, or clarify if there are specific limits or other constraints!

Would you like to calculate this for specific values of $N$, or need a more detailed explanation?

Here are some related questions for further exploration:

1. How does the convergence of the sum behave as $N$ increases?
2. Can this sum be approximated using integration techniques?
3. How does changing the power in the denominator affect the sum?
4. What happens when we generalize this for different values of $n$?
5. Could this sum be represented in closed form for specific values of $N$?

Tip: When working with summations, always double-check the limits of summation to clarify what is being summed.