Mathematics, 19.11.2019 04:31, aidanfbussiness

Which of the following are subspaces of r[infinity]? if not, explain why. a) all sequences such that |xj+1| ≥ |xj | for each j. b) all convergent sequences: the xj has a limit as j → [infinity]. c) all arithmetic progressions: xj+1 − xj is the same for all j. d) all geometric progressions: (x1, k x1, k2 x1, . .) allowing all k and x1

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Which of the following are subspaces of r[infinity]? if not, explain why. a) all sequences such tha...