Verify Summation in Christoffel Symbols Formula

[space-time]

In the formula for Christoffel symbols:

$\Gamma$^m_ij= $\frac{1}{2}$g^mk[(∂g_ki/∂x^j) + (∂g_jk/∂xⁱ) - (∂g_ij/∂x^k)

you do sum over k right?

I know this probably seems like a rather "noob-like" question and I know about Einstein summation convention. I am just asking because with previous Christoffel symbols I derived, they were in simple coordinate systems such as spherical and cylindrical, so I was just able to set k = m due to the fact that the metric tensors only had non-zero diagonal components.

 

[maajdl]

Yes, you sum over k.
That's because you raised the m index in this way, and raising an index work like that.
Further, once the Einstein convention is used, it is fully used.
You also forgot a closing square bracket.

 

[Matterwave]

A quick way to figure out whether something should be summed over is to look at the indices that appear on the left and the right hand sides. On the left there is m,i,j, on the right there is m,k,i,j so the k's must have been summed over or else they would appear on the left.