Prove a sequence S_n converges iff its tail S_n+M converges.
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Originally Posted by veronicak5678 Prove a sequence S_n converges iff its tail S_n+M converges. do you mean converges iff converges?
Yes, that's what I mean. Sorry I don't know Latex! So... any ideas?
Last edited by veronicak5678; August 13th 2011 at 04:53 PM.
Originally Posted by veronicak5678 Yes, that's what I mean. Sorry I don't know Latex! So... any ideas? you just have to use the definition of convergence. Assume . we will show that . gives us: To prove , that is: . We easily see that does the job. Now can you try and do the 'only if' part.
I see what I was doing wrong. Thanks everyone.
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