Let $(e\_n)\_{n\in \mathbb{N}}$ be unit vectors in a normed space X. I search for a sequence $(y\_k)\_{k\in \mathbb{N}}$ of convex combinations of the $(e\_n)\_{n\in\mathbb{N}}$, which converge strongly to $0$. Can someone give me an example?
I already showed the theorem:

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> Let $(x\_n)\_{n\in\mathbb{N}}$ be a sequence in X, which converges strongly to $x\in X$. There is a sequence of convex combinations of the $(x\_n)\_{n\in\mathbb{N}}$, which converges strongly to $x$. 
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But now I have to find a specific example. Can someone help me?