How can i derive step response in terms of impulse response from the convolution sum?
In an LTI system, any linear operation on inputs, is directly imposed on the outputs, that is, if an LTI system responses to $\delta[n]$ as $h[n]$, then it responses to $u[n]=\sum_{k=-\infty}^{n}\delta[k]$ as $s[n]=\sum_{k=-\infty}^{n}h[k]$.

This is also clear from the convolution since $$s[n]=u[n]*h[n]=\sum_{k=-\infty}^\infty h[k]u[n-k]=\sum_{k=-\infty}^n h[k]$$