Prove that if <a> converges, then every subsequence of <a> converges and has the same limit as a.
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Originally Posted by qtpipi Prove that if <a> converges, then every subsequence of <a> converges and has the same limit as a. let suppose that let be any subsequnce Since the sequence convereges there is an such that for all n > N but since if futher in the sequnce then so
Originally Posted by TheEmptySet but since if futher in the sequnce then so I'm not sure what you're saying here, can you rephrase it? Thanks
Originally Posted by qtpipi I'm not sure what you're saying here, can you rephrase it? Thanks The integer a subsequence has all of the same terms as the regular sequence. It just skips some ie and the first gives the sequence but the subsequce skips terms from the original so to get the term but So
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