# property of sum of coefs of a chain

Suppose c is a k+1 chain in U(open set in space R^n), then boundary of c (a k chain) can be expressed as a linear combination of k-cubes, using boundary operator: $$∂c=∑_ia_ic_i$$, where a_i are the coefs. Above is my understanding so far about relations brought by boundary operator, and now I am asked to show that sum of these coefs is 0, namely: $$∑_ia_i=0$$, I don't even see why this is even true. How should I approach this? Thanks for any suggestions.

• What is $U$ here? – 5xum Oct 22 '15 at 21:46
• Edited. It's open set in R^n – jfcjohn Oct 22 '15 at 21:49
• It's been a long time since I've dealt with this, but I'm pretty sure that the it results from the fact that $\partial^2 = 0$. – Paul Sinclair Oct 23 '15 at 0:01