# real analysis – Estimating the sine of the angles between vectors

Let $${s_n}$$ be a sequence of unit vectors in $$mathbb{R}^2$$ converging to some $$sinmathbb{R}^2$$. I want to show that $$sinmeasuredangle(s_n,s)le sum_{m=n}^inftysinmeasuredangle(s_m,s_{m+1})$$ for all $$n$$. This estimate makes intuitive sense from drawing a picture, but I am struggling to find a formal argument. Any suggestions would be appreciated.