# Taylor series, the convergence of sequence, and series of functions

Let Æ’n : R2 ï‚® R be Æ’n (x,y) = (x+y) / n

a. Show that Æ’n ï‚® 0 , but convergence is not uniform.

b. Show that the convergence Æ’n ï‚® 0 is uniform on bounded sets.

https://brainmass.com/math/real-analysis/convergence-sequence-series-functions-15063

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1. Let Æ’n : R2 ï‚® R be Æ’n (x,y) = (x+y) / n

a. Show that Æ’n ï‚® 0 , but convergence is not uniform.

Proof. Given , for any we know that there exists when , we have

.

So, , i.e., Æ’n ï‚® 0.

But from the proof, we know that ...

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