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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
Prove that a convergent sequence of real numbers is bounded.
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Arpan pal
If the sequence {Sn} is a convergent sequence and it convergence to l, then limSn=l. corresponding to £=1(≥0),there exists a natural number k such that 1-£⟨ Sn⟨1+£ for all n≥k Let U be the maximum of the set {S1,S1,S3,...Sk-1,1+£} Let L be the minimum of the set {S1,S2,S3,...Sk-1,1-£} Then L≤Sn≤U for all n≥k Thus the sequence {Sn} is bounded.