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## Homework Statement

We're asked to show that the geodesic equation [tex]\frac{du^{a}}{dt} +\Gamma^{a}_{bc}u^{b}u^{c}=0[/tex] can be written in the form [tex]\frac{du_{a}}{dt}=\frac{1}{2}(\partial_{a}g_{cd})u^{c}u^{d}[/tex]

## Homework Equations

[tex]\Gamma^{a}_{bc}=\frac{1}{2}g^{ad}(\partial_{b}g_{dc}+\partial_{c}g_{bd}-\partial_{d}g_{bc})[/tex]

## The Attempt at a Solution

I tried contracting the geodesic equation with [tex]g_{ab}[/tex] but came out with some Kronecker deltas which stumped me a bit.