How do I efficiently calculate the total sum with respect to a changing $\space v \space\space $in a square root $\sqrt{\dfrac {\hbar{((v)/(6.25E34))}}{4G}}r\space\large{?}$
The sum is based on the variable $\space "v"\space $ in the following expression which changes in increments of $\space 1\space $ with $\space vi=1\space \text{ to }\space vf=6.25E34.\quad$ Everything else in the expression is a constant.
\begin{equation} \sqrt{\frac{\hbar{((1)/(6.25E34))}}{4G}}r \\+ \sqrt{\frac{\hbar{((2)/(6.25E34))}}{4G}}r \\+ \sqrt{\frac{\hbar{((3)/(6.25E34))}}{4G}}r +\\ \cdots+ \sqrt{\frac{\hbar{((6.25E34)/(6.25E34))}}{4G}} r \\= \text{total} \end{equation}
To help give a visual aid the expression would operate as depicted here in the following illustration. ~ thank you.
