What is an example of a convergent series that does not have a sum of x?

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- Nov 20th 2013, 11:03 PMareyouseriousConvergent Series and Orthonormal Sets
What is an example of a convergent series that does not have a sum of x?

- Nov 26th 2013, 03:05 PMHallsofIvyRe: Convergent Series and Orthonormal Sets
If you just chose thing pretty much at random, you would probably get such an example. It is only as long as the vectors form an orthonormal basis for whatever vector space you are talking about that this sum

**will**be equal to x.

An example is , , and .