Sachin Kumar posted an Question
February 03, 2022 • 02:54 am 30 points
  • IIT JAM
  • Mathematics (MA)

Q.3 which of the following conditions implies (imply) the convergence of a sequence {xn} of real numbers? (a) given e> o there exists an to e n such that for al

Q.3 Which of the following conditions implies (imply) the convergence of a sequence {xn} of real numbers? (A) Given E> O there exists an to E N such that for all n 2 no. 1n+1-nl 0 there exists an 7to E N such that for all n2 no n+1a Xn+1n E (C) Givene> 0 there exists an no E N such that for all n 2 no» (n + 1)-|Xn+1- Xnl 0 there exists an o E N such that for all m, n with m>n2no 1XmXnl

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  • Anonymous User best-answer

    d since every convergent sequence is cauchy sequence according to defination for €>0 there exist n0 such that |xm-xn|<€

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    sir it is multiple correct answer.... c and d both is correct... but i don't understand what that all the options meaning... plz sir tell some solution of this definition besed questions

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    taking Xn=1+1/2+1/3+....+1/n then |Xn+1-xn|=1/n+1 <€ but {Xn} not convergent

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    |Xn+1-xn|<€(n+1)² for large n it is not possible so B not true

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    |Xn+1-xn|<€/(n+1)² <€ c true

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