If life is a series of experiences based on our karma, where is the doership for anybody?

That is true. It is ideal not to have the sense of doership at all. However we forget this very fact due to the veil of Maya and we tend to attach the sense of ownership to each and every act and each and every thing in our life, every moment of our life. That is the reason for all the sufferings. The true realization and experience of this fact will dawn only by the grace of God, which can be invoked easily through chanting the Mahamantra.