Hey guys I'm a bit new to GR and stuck on this question? :/. So we are given that: d2xi/dλ2+[itex]\Gamma[/itex]ijk dxi/dλ dxj/dλ = 0 and asked to show that d/dλ(gijdxi/dλdxj/dλ) = 0 So I expanded using the product rule to get: [itex]\Gamma[/itex]ijkd2xi/dλ2 dxj/dλ +[itex]\Gamma[/itex]ijk dxi/dλd2 xj/dλ2 Then rearranged the first equation to get: d2xi/dλ2 = - [itex]\Gamma[/itex]ijkdxi/dλ dxj/dλ and substituted for the second order differential equations. That's where I get stuck as I don't know how to get rid of the christoffel symbols. I read somewhere that they have a high degree of symmetry - so maybe I can change the dummy indices to get a symmetric form and they cancel? Very confused - any help would be appreciated.